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ILLUSTRATED 


First  iras  in  Irate, 


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\THOLIC  rilBLICATIOX  SOCIETY, 
„  No.  9  WARREN  STREET. 


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IN  MEMORIAM 
FLOR1AN  CAJORI 


THE 

YOUNG  CATHOLIC'S 

I ! 

ILLTJ8TEATED 

TABLE    BOOK 

AND 

FIRST  LESSONS  m  NUMBERS. 


N  EW  YORK  : 
THE    CATHOLIC   PUBLICATION   SOCIETY, 

9  WARREN  STREET. 

Boston  :  P.  DONAHOE.  Louisville  :  C.  A.  ROGERS. 

Baltimore  :  J.  MURPHY  &  Co.  San  Francisco :  M.  FLOOD. 

St.  Louis:  P.  Fox.  San  Jos6,  Cal. :  A.  WALDTEUFEL. 

Newark  ;  J.  J.  O'CONNOR  &  Co.  Portland,  Or.:  S.  J.  McCor.MicK. 


Entered,  according  to  Act  of  Congress,  in  the  year  1875,  by 

LAWRENCE    KEHOE, 
In  the  Office  of  the  Librarian  of  Congress,  at  Washington,  D.  C, 


u/ 


FIRST  LESSONS  IN  NUMBERS. 


COUNTING. 


LESSON   I. 

i.  A  single  thing  is  culled  a  Unit,  or  One. 

2.  A    Number  is 
one,    or   more  than 
one. 

3.  Figures       are 
Marks  used    to  ex- 
press n  umbers. 

4.  Counting  is  ex- 
pressing     numbers 
by  words. 

5.  How  many  dogs 
has  the  girl  in   the 
picture  ?  One. 

6.  How  many  eyes 
have     ou  ?       Two, 


6 


FIRST  LESSORS  AY  I 


7.  Two  cents  are   how  many  more  than  one 
cent  ? 

8.  If  you  had  two  cents  and  spent  them,  how 
many  would  you  hare  left  ? 

9.  How  many  are  two  pictures  and  one  pic- 
ture ?  Three. 

10.  Three  cents  are  how  many  more  than  two 
cents  ? 

11.  If  you  had  three   cents  and   spent  them, 
how  many  would  you  have  left  ? 

12.  How   many   are    three    pencils    and   one 
pencil  ?  Four. 

13.  Count  the  fingers  of  your  left  hand  :  how 
many  have  you  ? 

14.  Four    cents    are   how 
many      more      than      three 
cents  ? 

15.  Count    from     one    to 
four. 

1 6.  Count  from  four  back- 
to  naught. 

17.  Hold  up  four  fingers. 

18.  Copy    and     read    the 
figures      denoting      naught, 

one,  two,  three,  and  four. 

Printed  form,       01234 
Xame.  naught,     one,     two,     three,     four. 

Slate  form,.  0  1  %  •>  1 

19.  Which  figure  expresses  the  greatest  number 'i 


LESSORS  IN  NUMBERS. 
LESSON   II. 


1.  Calling  the   thumb  a    finger,  how   many 
fingers  have  you  on  your  righc  hand  ?  Five. 

2.  Five  cents  are  how  many  more 
than  four  cents  ? 

3.  Count  from  one  to  five. 

4.  Name  five  objects  or  things  in 
the  room. 

5.  How  many  are  five  boys  and  one  boy  ?    Six, 

6.  Six  is  how  many  more  than  five  ? 

7.  Count  from  one  to  six. 

8.  From  six  back  to  naught. 

9.  Draw  six  straight  lines  on  the  black-board. 
10.  Draw  one  more  :   how  many  are  six  lines 

and  one  line  ?  Seven, 

1  1.  Name  seven  boys  or  girls, 

12.  Count  from  one  to  seven. 

13.  From  seven  back  to  naught. 

14.  Place  seven  pencils  on  the  table  :  if  you 

place  one  more  with 
them,  how  many  will 
there  be  ?  Eight. 

15.  How  many  are 
seven  chickens  and  one 
chicken  ? 

1  6.  Eight  is  how 
many  more  than  seven? 
17.  Eight  is  how  many  more  than  one  ? 


8  FIRST  LESSORS  ix  X UMBERS. 

1 8.  Count  from  one  to  eight 

19.  From  eight  back  to  naught. 

20.  How   many  are     eight    oranges    and    one 
orange  ?  Nine. 

21.  What   comes   next    before    nine  ?      Before 
eight  ? 

22.  Count  from  three  to  nine.     From  live   to 
nine. 

23.  Copy   and  read   the   figures  denoting  five, 
six,  seven,  eight,  and  nine. 

Printed  form.       56  7  8*9 

Xame,  five,     nx,     seven,     eight,      nine. 

Slate  form,  J          0          r  3  9 

24.  Which  iigure  expresses  the  smallest  number? 

25.  Which  iigure  expresses  the  greatest  number? 


LKSSOX    III. 

1.  How  many  lingers  and  thumbs  have  you  on 
both  hands  ?  Ten, 

2.  Count  from  one  to 

ten.  f-fr 

3.  From    ten    back    to 
one. 

4.  Ten  is  one  more  than  what  number  ? 

5.  Count  by  twos  from  t\vo  :  as,  two,  four,  etc. 

6.  Count  by  twos- from  one  :  as,  one.  three,  etc, 


FIRST  LESSUSS  IN  S~I*MBERS. 


7.  Count  the  balls  on  the  upper  wire  of  the 
Numeral  Frame,  as  they  are  moved  from  left  to 
right. 


8.  How  many  will  one  ball  on  the  next  wire 
make  counted  with  the  ten  on  the  upper  wire  ? 

Eleven. 

9.  Two  balls  on  the  next  wire  counted  with 
the  ten  on  the  upper  wire  will  make  how  many  ? 

Twelve. 

10.  Three  balls  on  the  next  wire  counted  with 
the  ten,  will  make  how  many  ?  Thirteen, 


10  FIUST  LESXONS  IN  NCMBERS. 

11.  Four  balls  on  the  next  wire  counted  with 
the  ten,  will  make  how  many  ?  Fourteen. 

12.  Five  balls  with  the  ten,  how  many  ? 

Fifteen. 

13.  Six  balls  with  the  ten,  how  many  ? 

Sixteen. 

14.  Seven  balls  with  the  ten,  how  many  ? 

Seventeen. 

15.  Eight  balls  with  the  ten,  how  many  ? 

Eighteen. 

1 6.  Nine  balls  with  the  ten,  how  many  ? 

Nineteen. 

17.  Ten  balls  with  the  ten,  how  many  ? 

Twenty. 


LESSON  IV. 

1.  Ten  roses  and  one  rose  are  how  many  ? 

2.  Eleven  is  how  many  more  than  ten  ? 

3.  How  do  you  express  eleven  ? 

Ans.   By  writing  the  figure  i  with  a  figure  i  on 
the  right. 

4.  Ill  expressing  eleven,  how  many  figures  are 
used  ? 

5.  Eleven   peaches   and  one  peach   are   how 
many  ? 

6.  Count  from  one  to  twelve. 


FIRST  LESSONS  ix  NUMBERS.          11 

7.  How  do  you  express  twelve  ? 

Ans.    By  writing  the  figure  i  with  a  figure  2  on 
the  right. 

8.  Count  from  twelve  back  to  naught. 

9.  Count  by  threes  to  twelve. 

10.  Twelve  is  how  many  more  than  ten  ? 

11.  Show  by  the  numeral  frame  that  twelve  is 
two  more  than  ten. 

12.  Twelve  pears  and  one  pear  are  how  many  ? 

13.  Thirteen  is  how  many  more  than  ten  ? 

14.  Show  it  by  the  numeral  frame. 

15.  How  do  you  express  thirteen? 

1 6.  Thirteen  oranges  and  one  orange  'are  how 
many  ? 

17.  Fourteen  is  how  many  more  than  ten  ? 

1 8.  Show  it  by  the  numeral  frame. 

19.  How  do  you  express  fourteen  ? 

20.  Count  from  one  to  fourteen. 

21.  From  fourteen  back  to  one. 

22.  Copy  and  read  the  figures  denoting  ten, 
eleven,  twelve,  thirteen,  and  fourteen. 

io  ii  12  13  14 

ten,     eleven,     twelve,     thirteen,     fourteen. 
10          11  12  13  14 


1-'  /V//.ST  Lvssoxs  i\  J 

LHSSOX  V. 


1.  What  is  the  moaning  of  the  word  thirteen  ? 

Three  and  Ten, 

2.  What  is  the  meaning  of  the  word  fourteen? 

Four  and  Ten. 

3.  Count  by  twos  to  fourteen. 

4.  Fourteen  plums  and  one  plum   are   how 
many  ? 

5.  Fifteen  is  how  many  more  than  ten  ? 

6.  Show  it  by  the  numeral  frame. 

7.  How  do  you  express  fifteen  ? 

8.  Count  from  ten  to  fifteen. 

9.  How  many  cents  are  fifteen  cents  and  one 
cent  ? 

10.  Sixteen  is  how  many  more  than  ten  ? 

11.  Show  it  by  the  numeral  frame. 

12.  How  do  you  express  sixteen  ? 

13.  Count  from  ten  to  fifteen. 

14.  What  is  the  meaning  of  the  word  sixteen  ? 

15.  What  is  the  meaning  of  the  word  fifteen  ? 

Five  and  Ten. 

1  6.  How  many  dollars  are  sixteen  dollars  and 
one  dollar  ? 

17.  Seventeen  is  how  many  more  than  ten  ? 
1  8.  Show  it  by  the  numeral  frame. 

19.  Count  from  ten  to  seventeen. 

20.  How  do  you  express  seventeen  ? 

2j.  What  is  the  meaning  of  the  word  seven- 
teen ? 


FIRST  LESSORS  /.v  NUMBEUS.  13 


LESSON  VI. 

1.  How  many  men  arc  seventeen   men   and 
one  man  ? 

2.  Show  by  marks  on  the  black-board  that  ten 
and  eight  are  eighteen. 

3.  How  do  you  express  eighteen  ? 

.     4.  What  number  comes  next  after  eighteen  ? 

5.  Count  from  ten  to  nineteen. 

6.  How  do  you  express  nineteen  ? 

7.  What  is  the  meaning  of  the  word  nineteen? 

8.  What  number  comes  next  after  nineteen  ? 

9.  Twenty  is  how  many  more  ihan  ten  ? 


14  FIRST  LESSOXS  ix 


10.  Copy  and  read  the  figures  denoting  fifteen, 
sixteen,  seventeen,  eighteen,  nineteen. 

1~>  10  i:  18  19 

11.  Copy  and  compare  the  following  : 

0  *10 

1  11        Eleven  is  10  more  than  i. 

2  12        Twelve  is  10  and  2. 

3  13        Thirteen  is  10  more  than  3. 

4  14        Fourteen  is  10  more  than  4. 

5  15        Fifteen  is  10  more  than  5. 

6  JO        Sixteen  is  6  more  than  10. 

7  77        Seventeen  is  7  more  than  10. 

8  18        Eighteen  is  8  and  10. 

9  J$        Nineteen  is  9  more  than  TO. 

Test  the  pupil's  knowledge  of  the  above  groups  by  allow- 
ing him  to  read  them  in  order,  down  and  up,  and  out  of  order. 


LESSON  VII. 

1.  What  is  the  meaning  of  the  word  twenty  : 

Two  Tens. 

2.  How  do  you  express  twenty  '? 

3.  In   expressing   twenty,  how  many  figures 
are  used  ? 

4.  What  is   the   figure   <»n    the   right  called  r 

Naught. 

5.  What  figure  is  in  the  second  place  ?     Two. 


FIRST  LESSONS  IN  NUMBERS.          15 

6.  Draw  ten  marks  on  the  black-board. 

7.  Draw  ten  more,  and  count  how  many  there 
are  in  both  rows. 

8.  If  you  draw  one  more,  how  many  ? 

Twenty-one. 

9.  If  you  draw  one  more,  how  many  ? 

Twenty-two. 

10.  Another,    how  many  ?     (Continue  to  29.) 

Twenty-three. 

n.   Twenty-nine    is    how    many    more    than 
twenty  ? 

12.  How  do  you  express  twenty-one,  etc,? 

13.  Count  from  twenty  to  twenty-nine. 

14.  Copy  and  read  the  figures  denoting  twenty, 
twenty-one,  etc. 

20  21  22  23 

twenty,    twenty-one,    twenty-two,    twenty-three, 

24  25  26  27 

twenty-four,  twenty-five,  twenty-six,  twenty-seven, 

28  29 

twenty-eight,  twenty-nine. 

1 5.  Copy  and  compare  the  following  : 

0  10  20 

1  11  21 

2  12  22 

3  13  23 

4  14  24 
Etc. 

9  19  29 


1G          FixsT  LESSONS  IN  NUMBERS. 
LESSON   VIII. 

1.  What,  is  the  meaning  of  the  word  thirty  ? 

Three  Tens. 

2.  In  expressing  thirty  how  many  figures  are 
used  ? 

3.  What  is  the  figure  on  the  right  called  ? 

4.  What  figure  is  in  the  second  place  ? 

5.  Count  from  thirty  to  thirty-nine. 

6.  Thirty  is  how  many  more  than  twenty  ? 

7.  How  many  more  than  twenty-nine  ? 

8.  Write  the  figures  denoting  thirty,  thirty- 
one,  thirty-two,  etc. 

9.  How  do  you  express  thirty-two  ? 

10.  How  do  you  express  twenty-three  ? 

11.  Copy  and  compare  the  following  : 

0  10  20  30 

1  11  21  31 
I  1.2  23  32 

Etc. 

9  10  29  39 

12.  What   number   comes    next    after  thirty- 
nine  ?  Forty. 

13.  What  is  the  meaning  of  the  word  forty  ? 

Four  Tens. 

14.  In  expressing  forty,  what  figure  occupies 
the  second  place  ? 

15.  Count  from  forty  to  forty-nine. 


FIRST  LESSONS  IN  NUMBERS.          17 

1 6.  Write  the   figures  denoting  forty,   forty- 
one,  forty-two,  etc. 

17.  Copy  and  compare  the  following: 


0 

10 

20 

30 

40 

1 

11 

21 

31 

41 

2 

12 

22 

32 

& 

8 

13 

23 

33 

43 

Etc. 

9 

'19 

29 

39 

49 

LESSON  IX. 

1.  Count  from  one  to  one  hundred. 

2.  Count  by  twos  to  one  hundred. 

3.  In  one  hundred,  what  is  the  figure  on  the 
right  called  ? 

4.  What  figure  is  in  the  second  place  ? 

5.  What  figure  is  in  the  third  place  ? 

6.  If  a  man  had  a  hundred  dollars  and  earned 
a  hundred  more,  how  many  dollars  would  he 
have?  Two  hundred. 

7.  In   expressing  two  hundred,    how  many 
figures  are  used  ? 

8.  What  figure  is  in  the  first  place  ?    Second  ? 
Third  ? 

9.  Two  hundred  and  one  hundred  are  how 
many  ? 


18          FIRST  LESSORS  nv  NUMBERS. 

10.  How  is  three  hundred  expressed  ? 

By  writing  three  in  the  third  place,  naught  in 
the  second  place,  and  naught  in  the  first  place. 

11.  How  is  four  hundred  expressed  ? 

12.  Five  hundred  ?          13.  Six  hundred  ? 

14.  Seven  hundred  ?        15.  Eight  hundred  ? 

1 5.  Nine  hundred  ? 

Ans.  By  writing  the  figure  9  with  two  naughts  on 
the  right. 

17.  Count  by  hundreds  from  one  hundred  to 
nine  hundred. 

1 8.  Copy  and  read  : 

100    200    300    400    500     600     700    800     900 

19.  Copy  and  compare  the  following  : 

0  10  100 

2  20  200 

3  30  300 
Etc. 

9  00  000 


LESSON   X. 

1.  A  man  spent  $100  for  a  horse  and  one  dollar 
for  a  whip  ;  how  many  dollars  did  he  spend  ? 

One  hundred  and  one  dollars. 

2.  How  is  one  hundred  and  one  expressed  ? 
By  writing  one  in  the  third  place,  naught  in  the 
second  place,  and  one  in  the  first  place. 


FIRST  LESSONS  IN  NUMBERS.          19 

3.  Count  from  one  hundred  to  one  hundred 
and  nine. 

4.  Copy  and  read  the  following  : 

100   101    102    103    104    105    106    107    108    109 

5.  What  number  comes  next  after  109  ? 

One  hundred  and  ten. 

6.  Count  from  no  to  119. 

7.  Copy  and  read  the  figures  denoting  one  hun- 
dred and  ten,  etc.,  to  one  hundred  and  nineteen. 

8.  Copy  and  compare  : 

100  110 

101  111 

102  112 
Etc. 

109  119 

9.  What  number  comes  next  after  119  ? 
10.  Count  from  120  to  129. 
n.  Copy  and  read  : 
120    121    122    123    124    125    126    127   128   129 

12.  Compare: 

100  110  120 

101  111  121 

102  112  122 
Etc. 

109       119       129 

13.  One  hundred  and  nineteen  is  how  many 
more  than  one  hundred  and  nine  ? 

14.  One  hundred  and  twenty-nine  is  how  many 
more  than  one  hundred  and  nine  ? 


20          FIRST  LESSONS  IN 


LESSON   XL 

1.  Notation  is  the  art  of  writing  numbers. 

2.  Numbers  are  written  or  expressed  by  words, 
letters,  or  figures. 

3.  The  method  of  writing  or  expressing  num- 
bers by  letters  is  called  the  Roman  Method, 

4.  The  method  of  writing  or  expressing  num- 
bers by  figures  is  called  the  Arabic  Method. 

5.  The   Roman  Method  of  Notation  employs 
seven  capital  letters  to  express  numbers. 

6.  The  letter  I,  denotes  one ;  V,  five ;  X,  ten ; 
L,  fifty ;  C,  one  hundred ;  D,  five  hundred ;  and 
M,  one  thousand. 

7.  Other  numbers  are  expressed  by  repeating 
and  combining  these  capitals. 

8.  Repeating  a  letter  repeats   its   value ;   as, 
XXX,  thirty. 

9.  If  a  letter  is  placed  before  one  of  greater 
value,  the  value  of  the  less  is  taken  from  the 
greater ;  as,  XL,  forty. 

10.  If  a  letter  is  placed  after  one  of  greater 
value,  the  value    of    the  less  is  added  to  the 
greater,  as,  LX,  sixty. 

n.  The  Roman  Method  of  Notation  is  used  in 
numbering  the  chapters,  lessons,  etc.,  into  which 
books  are  divided,  and  in  marking  the  hours  on 
clocks  and  watches. 


* LESSONS  /.v  NUMBERS. 
LESSON   XII. 

TABLE  OF   JIOMAST   XOTATION. 


I            one. 

XXV      twenty-five. 

II          two. 

XXVI     twenty-six. 

Ill        three. 

XXVII   twenty-seven. 

IV         four. 

XXVIII  twenty-eight. 

V          five. 

XXIX     twenty-nine. 

VI        six. 

XXX       thirty. 

VII       seven. 

XL           forty. 

VIII     eight. 

L              fifty. 

IX        nine. 

LIX         fifty-nine. 

X          ten. 

LX           sixty. 

XI        eleven. 

LXX       seventy. 

XII      twelve. 

LXXX    eighty. 

XIII     thirteen. 

XC          ninety. 

XIV     fourteen. 

C              one  hundred. 

XV       fifteen. 

CO           two  hundred. 

XVI     sixteen. 

COG         three  hundred. 

XVII  seventeen. 

CD           four  hundred. 

XVIII  eighteen. 

D              five  hundred. 

XIX     nineteen. 

DC           six  hundred. 

XX       twenty. 

DCC        seven  hundred. 

XXI     twenty-one. 

DCCC     eight  hundred. 

XXII    twenty-two. 

CM          nine  hundred. 

XXIII  twenty-three. 

M             one  thousand. 

XXIV  twenty-four. 

MM          two  thousand. 

MDCCCLXXVI   one 

thousand    ei^lit    hundred 

and  seventy-six. 


FIRST  Licssoxs  /.v 


LESSON  XIII. 

1.  Express  35  by  letters.  XXXV. 

2.  In  XXXV,  how  often  is  X  repeated  ? 

Three  times. 

3.  Express  59  by  letters.  LIX. 

4.  Erom  which  letter  is  the  value  of  I  taken  ? 

5.  Copy  and  read  the  following  numbers : 

III.  XVI.  XLV. 

VI.  XXIV.  LXIX. 

VIII.  XXXVI.          CIV. 

6.  The  face  of  a  clock  is  divided  into  twelve 
equal  parts,  marked  by  the   letters   I,   II,  III, 
IV,  V,  VI,  VII,  VIII,  etc. 

7.  The  short  hand  points 
to  the  hours,  and  is  called 
the  hour  hand. 

8.  The  long  hand   points 
out    the     minutes,    and    is 
called  the  minnte  hand. 

9.  The  hour  hand  moves 
from    one    number    to    the 
next  in  one  hour. 

10.  If  the  hour  hand  is  at 

XII,   what  time   is  it  when   the   minute   hand 
moves  to  I  ?  It  is  five  minutes  past  twelve. 

11.  When  the  minute  hand  moves  to  II  ? 

Ten  minutes  past  twelve. 

12.  When  the  minute  hand  moves  to  VI  ? 

Half-past  twelve. 


FIRST  LESSONS  IN  NUMBERS.          ;M 
LESSON   XIV. 

ARABIC    XOTATIOX. 

1.  The  Arabic  Method  of  Notation  employs 
ten  figures  to  express  numbers.     These  figures 
were  brought  into  Europe  from  Arabia. 

0123456789 

2.  The  figures  from  i  to  9  are  called  signifi- 
cant figures,  because  each  has  a  value  of  its  own. 

3.  They  are  also  called  digits,  because  the 
ancients   reckoned   on  their   fingers   (digitus,  a 
finger). 

4.  The  first  is  called  naught,  because   when 
standing  alone  it  has  no  value.     It  is  also  called 
zero  or   cipher.     Nine  is  the  greatest  number 
expressed  by  a  single  figure. 

5.  The   significant  figures    are    called  units, 
or  figures  of    the  first  order.     Numbers  greater 
than  ten  form  higher  orders  of  units,  called  tens, 
hundreds,  thousands,  etc. 

6.  Ten  is  expressed  by  writing  i  in  the  second 
place,  with  a  naught  on  the  right :  as,  10. 

7.  Figures    standing  in  the  second  place  are 
called  tens,  or  units  of  the  second  order. 

8.  A  hundred  is  expressed  by  writing  i  in  the 
third  place,  with  two  naughts  on  the  right. 

9.  Figures  standing   in   the   third   place   are 
called  hundreds,  or  figures  of  the  third  order. 


10.  Three  figures  form  a  period. 

11.  In    every    period    the    right-hand    figure 
represents    units,   the   middle   figure   represents 
tens,   and  the  left-hand  figure   represents   hun- 
dreds. 

12.  What  is  the  rule  for  expressing  numbers  of  figures  ? 
Begin  at  the  left,  and  write  the  figures  of  the 

given  orders  in  their  places  toward  the  right. 
When  intermediate  orders  are  omitted,  supply 
their  place  with  naughts. 


LESSON  XV.  . 

XUMERATIOX. 

1.  Numeration  is  the  art  of  reading  numbers. 

2.  In  the  French  Method  of  Numeration  three 
orders  form  a  period. 

3.  Numbers  are  read  by  naming  the  figures, 
the  places  they  occupy,  and  the  period  in  which 
they  stand. 

4.  What  is  the  rule  for  reading  numbers? 

Divide  them  into  periods  of  three  figures 
each,  beginning  at  the  right. 

Beginning  at  the  left,  read  the  periods  in 
succession,  calling  each  by  its  proper  name. 


LESSONS  ix  NUMBERS. 


NUMERATION   TABLE. 


34 

Period.           2d 

Period.          ist 

Period. 

—  \ 

CO* 

r~ 

CO 

'2 

O 

c3 

13 

i 

| 

g 

CO 

g 

H 

1 

«w 

2 

0 

0 

3 

to 

rS 

H 

1      -s 

CP 

r2 

0) 

O 

CO 

Pi 

H 

O 

f^ 

1 

0 
CO 

5 

1  l  i 

i 

1 

H 

H 

»       w 

H 

H           W 

H 

P 

9 

8 

7,         6 

5 

4.         3 

2 

I. 

Millions 

Thousands, 

Units. 

This  is  read  nine  hundred  and  eighty-seven 
million,  six  hundred  and  fifty-four  thousand, 
three  hundred  and  twenty-one. 

5.  Recite  the  table.     Copy  and  read  i 
(6.)  (7.)  (8.)  (9.)  (10.) 

131  190  3176  1021 

118  600  1041  9010 

636 1  309  6360  3007 

Write  in  figures  nine  thousand  and  thirty- 


117 

234 
607 
ii. 
four. 

12. 


Six  thousand,  one  hundred  and  four. 

13.  Ninety    thousand,     seven     hundred,     and 
twenty-nine. 

14.  One  million,  one  thousand,  one  hundred 
and  twenty-five. 


FIRST  LESSONS  ix  NU 


AH    EXEECISE    WITH    OOTJ1TTEBS. 

LESSON  XVI. 

ORDINAL    XUMBERS. 

The  words  first,  second,  third,  etc.,  are  called 
Ordinal  Numbers.  They  denote  the  order  in 
which  objects  are  arranged. 

Name   the  seven  days  of  the  week. 

What  day  of  the  week  is  Sunday  ?  Monday  ? 
Tuesday  ?  Wednesday  ?  etc. 

Name  the  first  month,  second,  etc. 

What  is  the  name  of  the  first  period,  second, 
third,  etc. 


FIRST  LESSONS  IN  NUMBERS. 


ADDITION. 


LESSOR   I. 

1.  Addition  is  the  process  of, uniting  several 
numbers  into  one  sum. 

2.  The  Sum,  or  Amount,  is  tlio  result  or  num- 
ber obtained.      It  is  equal  to   all   the   numbers 
added. 

3.  The   Sign   of  Addition   is   a  perpendicular 
cross  +,  and  is  called  plus,  which  means  more. 
Placed  between  two  numbers,  it  shows  that  they 
are  to  be  added  together. 


28  FIRST  LESSORS  /.v  X 

LESSOX  II. 


Principles,—!.  Only  like  Numbers  can  be 
added,  2.  The  sum  and  the  numbers  added 
must  be  like  numbers. 

0  and    i    are   i.  6   and    i    are    7. 

1  "      i     "     2.  7     "      i     "     8. 

2  "         I        "       3.  S        "         I        "       9.       » 

3  "      i     "     4.  9     "      i     "  10. 

4  '*'       i      "     5.  10     •'•'      i      "  ii. 

5  "      i     "     6.  ii     "      i     <;   12. 

1.  George  has  2  books  on  the  seat  and  i  book 
in  his  hand  :  how  many  has  he  in  all  ? 

Solution. — 2  books  and  1  book  are  3  books. 

2.  How  many  are  4  horses  and  one  horse  ? 

3.  If  you  have  5  pencils  and  your  teacher  gives 
you  one  more,  how  many  will  you  have  ? 

Solution. — I  will  have  the  sum  of  five  pencils 
and  one  pencil,  which  is  six  pencils. 

(4.)      (5.)      (6.)      (7.)     (8.)     (9.)     (10.)     (n.) 
01234         o  6 

111111  1          1 

12.  The  sign  of  equality  is  two  short  parallel 
lines  zi.      It  is  read   equals  or   equal.     Placed 
between  two  numbers,  it  denotes  that  they  equal 
each  other.     It  may  be  read  5+1  are  6. 

13.  The  dollar  sign  is  an  S  and  two  parallel  lines 
drawn  through  it :  thus,  $. 


FIRST  LESSORS  ix  NUMBERS.  29 

LESSON  III. 

0  and  z  are   2.  6  and  2   are  8. 

1  "     2     "    3.  7     "     2     "    9. 

2  "         2        "       4.  8       "         2        "    10. 
'3       "         2       "       5.  9       "         2        "    II. 

4  "        2       "       6.  10       "        2       "    12. 

5  "     2     "    ?.  ii     "      2     "  13. 

1.  Three  windows  and  one  window  are  how 
many  ? 

2.  If  John  has  4  books,  and  buys  2  more,  how 
many  will  he  have  ? 

3.  How  many  are  5  slates  and  2  slates  ? 

4.  How  many  are  7  desks  and  2  desks  ? 

5.  Show  that  8  pencils  and  2  pencils  are  10 
pencils. 

6.  A  boy  had  9  cents,  and  earned  two  more  : 
how  many  did  he  then  have  ? 

7.  Mary  has  n  cherries,  and  Kate  has  2  cher- 
ries :  how  many  cherries  have  both  girls  ? 

8.  John  had  2  apples,  his  sister  had  5,  and  his 
brother  had  two  :  how  many  had  all  ? 

Copy  and  complete  the  following  : 
(9.)    (10.)    (ii.)    (12.)    (13.)    (14.)     (15.)   (16.) 
01234          567 
22222222 


20.  Count  by  twos  till  you  reach  60. 


30  FIRST  LESSONS  IN  NUMBERS. 

LESSON  IV. 

0  and  3  are  3.  6  and  3  are  9. 

1  "  3  "  4-  7  "  3  "  i°- 

2  "  3  "  5-  8  "  3  "  ii. 

3  "  3  "  6-  9  "  3  "  J2- 

4  "  3  "  7.  10  "  3  "  13. 

5  "      3     "     8-  ii     "      3     "  14- 

1.  Two  coats  and  three  coats  are  how  many  ? 

2.  Show  that  4  pencils  and   3   pencils  are  7 
pencils. 

3.  There  are  6  skates  in  one  window  and  3 
skates  in  another :  how  many  are  in  both  win- 
dows ? 

4.  There  were  7  houses  in  one  street,  and  they 
are  building  3  new  houses:  IIOAV  many  will  there 
be  when  these  are  finished  ? 

5.  A  man  had  9  cows,  and  bought  three  more  : 
how  many  did  he  then  have  ? 

6.  Count   by    threes,  beginning   with    three: 
thus,  3,  6,  9,  etc. 

7.  Count  by  threes,  from  one.    From  two. 

8.  Eleven  cents  and  three  cents  are  how  many  ? 

9.  Write  the  table  thus :  0+3=3. 
Copy  and  complete  the  following  : 

(10.)   (n.)   (12.)    (13.)   (14.)    (15.)    (16.)    (17.) 
0123456          7 


FIRST  LESSONS  IN  NUMBERS.          31 

LESSON  V. 

0  and  4   are  4.  6   and  4  are    10. 

1  "      4     "     5-  7     "     4     "     ii. 

2  "      4     "     6.       .        8     "      4     "     12. 

3  "      4     "     7.  9     "      4     "     13- 

4  "      4     "     8.  10     "      4     "     14. 

5  "      4     "     9-  ii      "      4     "     15- 

1.  One  ship  and  four  ships  are  how  many  ? 

2.  Two  masts  and  four  masts  are  how  many  ? 

3.  Five  ropes  and  four  ropes  are  how  many  ? 

4.  Show  that  3  books  and  4  books  are  seven 
books. 

5.  Six  houses  and  four  houses  are  how  many  ? 

6.  Seven  men  were  in  one  boat  and  four  in  an- 
other :  how  many  were  in  both  ? 

7.  The  tail  of  a  boy's  kite  was  ten  feet  long  ; 
lie  tied  on  four  feet  :  what  was  its  whole  length  ? 

8.  A  man  had  4  dollars,  and  he  earned  9  dol- 
lars :  how  many  did  he  then  have  ? 

Solution.—  He  had  the  sum  of  $4  and  $9, 
which  is  13  dollars  ;  Or  he  had  $13,  because  $4 
and  $9  are  $13. 

Copy  and  complete  the  following  : 
(9.)    (10.)    (n.)    (12.)    (13.)    (HO    (15-)    (16.) 

?        3        I      ,5        6         7        8        9 

44444444 


(17.},  l 

20.  Count  by  fours  till  you  reach  60. 


'32  FIRST  LESSONS  IN  L 

LESSON    VI. 


0  and   5   are  5.  6   and   5   are    n. 

1  «      5     "     6.  7     <•'      5     "•     12. 
2-5-7.  8-5     «     13. 

3  "      5     "     8-  9     "      5     "     H. 

4  "      5     "     9-  I0     "      5     "     T5- 

5  "      5     "  10.  ii     "      5     "     1  6. 

1.  Two  boys  and  five  boys  are  how  many  ? 

2.  Show  by  lines  on  the  black-board  that  three 
and  five  are  eight. 

3.  One  room  has  5  windows,  and  another  has 
6  :  how  many  windows  in  both  rooms  ? 

4.  There  are  5  houses  in  one  row  and  7  in 
another  :  how  many  in  both  ? 

5.  I  counted  8  apples  on  one  branch  and  5  on 
the  next  :  how  many  on  both  ? 

6.  There  are  5  peaches  in  one  basket  and  9  in 
another  :  how  many  in  both  ? 

7.  James  caught  10  fish,  and  his  brother  caught 
5  :  how  many  did  both  catch  ? 

8.  Edward  is  7  years  old  :  how  old  will  he  be 
5  years  hence  ? 

9.  If  you  are  9  years  old  and  your  brother  is 
5  years  older  than  you,  how  old  is  your  brother  ? 

(10.)    (n.)    (M.M.I3.)  (14-)  (15.)  (16.)  (17.) 

0123  4          •>          #         7 

1          111  1          J          11 

o  ~>          .7         -7  -7          5          5         5 


FIRST  LESSONS  IN  NUMBERS.  33 

LESSON  VII. 


o  and  6  are   6. 

6  and  6  are  12. 

i     «    6     "     7. 

7     «     6     «     13. 

2     "     6     "     8. 

8     "     6     "     14. 

3     «     6     "     9. 

9     «     6     «     15. 

4     "     6     "   10. 

10     "     6     "     1  6. 

5     "     6     "ii. 

ii     "     6     "     17. 

1.  If  you  have  3  peaches  and  buy  6  more,  how 
many  will  you  have  ? 

2.  How  many  are  6  cents  and  7  cents. 

3.  There  are  4  buds  on  one  bush  and  6  on  an- 
other :  how  many  on  both  ? 

4.  Charles  paid  6  cents  for  ink  and  8  cents  for 
paper:  how  many  cents  did  he  spend  ? 

5.  How  many  cents  must  a  boy  have  to  buy 
ten  cents'  worth  of  cake  and  6  cents'  worth  of 
candy  ? 

6.  How  many  cents  must  I  give  a  boy  if  I  wish 
him  to  buy  a  spool  of  thread  at  6  cents  and  a 
yard  of  muslin  at  1  1  cents  ? 

Copy  and  complete  the  following  : 
(7.)      (8.)     (9.)      (10.)      (ii.)      (12.)      (13.)    (14.) 
67896  6  66 

11110  1  23 

66662  2  22 


(15.)  4 

17.  Count  by  lives  till  you  reach  60,    By  6's. 


34          FIRST  LESSONS  IN  NUMBERS. 
LESSON  VIII. 

0  and  7   are   7.  6   and   7   are   13. 

1  "      7     "     8.  7     "      7     "     14. 

2  "  7  "  9-  8  "  7  "  J5. 

3  "  7  "  jo.  9  "  7  "  16. 

4  "  7  "  ii.  10  "  7  "  17. 

5  "  7  "  12.  ii  "  7  "  18. 

1.  How  many  are  3  cents  and  7  cents  ? 

2.  Count  by  sevens  till  you  reach  70. 

3.  How  many  are  $5  and  $7  ? 

4.  Three  sheep  are  in  one  field  and  seven  in 
another :  how  many  are  in  both  ? 

5.  There  are  6  trees  in  one  row  and  7  in  an- 
other :  how  many  are  there  in  the  two  rows  ? 

6.  James  spent  7  cents  for  pencils  and  8  for  a 
slate :   how  much  money  did  he  spend  ? 

7.  A  boy  had  9  cents   left  after  spending  7 
cents  :  how  many  cents  did  he  have  at  first  ? 

8.  There   are    10   boys  in  one  line  and  7  in 
another  ;   how  many  in  both  ? 

9.  A  boy  missed  7  words  and  recited  1 1  :  how 
many  words  was  he  asked  to  spell  ? 

10.  A  railroad  train  was  made  up  of  7  passen- 
ger cars,  and  10  freight  cars  :  how  many  in  all  ? 

(n.)   (12.)   (13.)   (14.)   (15.)   (16.)   (17.)   (18.) 
01234          50          7 

77777          77 


FIRST  LESSONS  IN  fi 

LESSOR  IX. 

0  and  8  are    8.  6  and  8  are  14. 

1  «  8  «  9.  7  "  8  «  15. 

2  "  8  "  10.  8  "  8  "  16. 

3  "  8  "  n.  9  "  8  "  17. 

4  "  8  "  12.  10  "  8  "  1 8. 

5  "  8  "  13.  ii  "  8  "  19. 

1.  How  many  are  $i  and  $8  ? 

2.  There  are  2  birds  on  the  fence  and  8  on  the 
tree :  how  many  are  there  in  all  ? 

3.  A  sponge  cost  3  cents  and  a  rubber  8  cents  : 
how  many  cents  did  both  cost  ? 

4.  There  are  8  windows  in  the  front  of  a  house 
and  4  in  the  rear  :  how  many  are  there  in  all  ? 

5.  John  gaye  away  5  peaches  and  has  8  left  : 
how  many  had  he  at  first  ? 

6.  Six  years  ago  John  was  8  years  old  :  how 
old  is  he  now  ? 

7.  How  many  are  7  yards  and  8  yards  ? 

8.  After  selling  8  turkeys,  a  farmer  has  8  left : 
how  many  had  he  at  first  ? 

9.  How  many  are  9  and  8  ?   10  and  8  ?  n  and 
8  ?  12  and  8  ? 

10.  Count  by  eights  till  you  reach  80. 

(ii.)    (12.)    (13.)    (14.)    (I5-)    (16.)    (17-)    (18.) 
01334507 
88888888 

(19.)  8+4+8+2=?         (20.)  f)+l+3+S+l=:? 


LESSON  A. 

0  and  9  are   9.  6  and   9  are  15. 

1  *'•  9  <%   10.  7  "'     9  "  *6. 

2  "  9  "  ii.  8  "     9  "  17. 

3  "  9  "  12.  9  "     9  "  18. 

4  "      9     "  J3-  Jo     "     9     "     I9- 

5  "      9     "  14.  ii     "     9     "     20. 

i«  A  boy  was  sent  for  one  pound  of  tea  and  9 
pounds  of  sugar:  how  many  pounds  must  lie 
carry  home  ? 

2.  There  are  9  persons  in  one  family  and  8  in 
another:  how  many  persons  in  the  two  families  ? 

3.  Henry's  hat  cost  §2  and  his  coat  $9  :  how 
many  dollars  did  both  cost  ? 

4.  Count  by  nines  till  you  reach  90. 

5.  Mary  is  four  years  old,  and  Kate  was  nine 
years  \vhen  Mary  was  born :  how  old  is  Kate  ? 

6.  After  giving  away  5  roses,  Jane  has  9  left : 
how  many  had  she  at  first  ? 

7.  If  a  quart  of  apples  cost  6  cents  and  a  quart 
of  pears  cost  9  cents,  what  will  both  cost  ? 

8.  Count  by  tens  till  you  reach  100. 

9.  Paid  88  for  a  tableland  89  for  six  chairs: 
how  many  dollars  did  I  spend  ? 

10.  Charles  and  Edward  had  9  marbles  each; 
Charles  gave  his  to  Edward  :  how  many  did  Ed- 
ward then  have  ? 

11.  Ten  persons  sat  on  one  side -of  a  car  and  9 
on  the  other :  how  many  persons  were  in  the  car  ? 


FIKST  LESSONS  /.Y  NUMBERS.          37 
LESSON  XL 

To  add  single   columns. 

i.  Find  the  amount  of  8,  3,  i,  4,  9.    Slatework. 

ANALYSIS.— i.  Write  the  numbers  one  under  8 

another,  in  a  perpendicular  column,  and  draw  3 

a  line  underneath.  i 

2.  Begin  at  the  bottom  and  add  the  numbers  4 
to  one  another,  thus:  9,  13,  14,  17,  25.  9 

3.  Write  the  amount  underneath. 

Hence  the  sum  is  25.  25  Ans. 

NOTES. — i.   In  adding,  name  the  results  only.     Avoid 
this  style:  9  and  4  are  13,  and  i  are  14. 

2.  Require  the  pupil  to  add  without  counting  fingers  or 
other  objects. 

3.  Insist  on  neat  figures  and  perpendicular  columns. 

(*•)  (3.)  (4.)  (5-)  (6.)  (7.)  (3.)  (9-) 
3  345 

222224_c6 

67899567 

12  45678 

(10.)  (II.)  (12.)  (I3.)  (I4.)  (IS.)  (.6.)  (I7.) 


5 

6 

7 

8 

9 

7 

8 

9 

4 

4 

4 

4 

4 

8 

9 

7 

6 

6 

6 

6 

6 

9 

7 

8 

7 

9 

7 

9 

8 

7 

8 

9 

9 

8 

9 

6 

5 

8 

9 

8 

2 

3 

4 

5 

6 

9 

8 

7 

38  FIRST  LESSONS  ix  XUXHKKS. 

LESSON  XII. 
(i.)     (2.)    (3.)     (4.)     (5.)    (6.)     (7.)     (3.) 


6 

6 

6 

6 

6 

6 

6 

6 

5 

8 

7 

9 

4 

6 

6 

7 

6 

6 

6 

6 

6 

7 

6 

7 

8 

7 

8 

6 

8 

7 

7 

6 

6 

6 

6 

7 

9 

8 

7 

8 

7 

5 

9 

9 

8 

8 

8 

8 

5 

8 

8 

7 

7 

8 

8 

6 

6 

4 

9 

8 

9 

9 

9 

9 

7 

8 

9 

6 

8 

9 

9 

9 

7 

8 

9 

8 

9 

9 

9 

9 

(9-) 

(10.) 

(n.) 

(12.) 

(13.) 

(14.) 

('5-) 

(16.) 

3 

7 

9 

7 

4 

i 

H 

9 

6 

14 

12 

i 

9 

9 

8 

3 

8 

9 

7 

H 

7 

8 

13 

16 

ii 

3 

i 

9 

13 

15 

9 

4 

4 

i 

4 

4 

8 

6 

7 

8 

(~) 

(18.) 

(190 

(20.) 

(21.) 

(22.) 

(23.) 

(24.) 

8 

5 

8 

5 

6 

8 

7 

9 

7 

9 

5 

6  ' 

5 

9 

8 

6 

9 

16 

7 

T7 

7 

25 

9 

18 

15 

8 

6 

9 

J3 

9 

6 

5 

9 

7 

9 

8 

9 

7 

18 

9 

4 

6 

13 

7 

8 

6 

9 

8 

FIRST  LESSONS  IN  NUMBERS.          39 

LESSON  XIII. 

When  the  sum  of  each  column  is  less  than  10. 
i.  What  is  the  amount  of  521  and  126  ? 

ANALYSIS. — i.  Write  the  numbers  one  un-  Slate  work. 

der  another,  units  under  units,  tens  under  521 

tens,  etc.,  and  draw  a  line  underneath.  126 

2.  Add  the  figures  in  the  units'  column,        

and  write  the  sum,  which  is  7  units,  under  647  Ans. 
units'  place. 

3.  Add  the  figures  in  the  tens'  column,  and  write  the 
sum,  which  is  4  tens,  under  the  tens'  place. 

Continue  thus  until  all  the  columns  are  added. 
Hence  the  sum  is  647. 

(2.)       (3.)       (4.)       (5.)       (6.)      (7.)      (8.) 


12 

22 

32 

48    15 

17 

234 

13 

23 

33 

10    71 

40 

123 

14 

24 

34 

21      12 

31 

43° 

(9.) 

(10.) 

(n.) 

(I2-)   (I3-) 

(I4.) 

(is-) 

I05 

341 

301 

142    364 

132 

307 

56i 

"3 

65 

32O    2O2 

43 

172 

323 

202 

5^3 

5l6   423 

704 

520 

(16.) 

(I?-) 

(i&; 

)  '  (190 

(20.) 

(21.) 

$    Pounds.   Men 

Miles. 

Acres. 

Horses. 

234 

230 

561 

35 

802 

240 

140 

614 

*5 

9*3 

9l 

5  '4 

405 

*35 

3°3 

S1 

1  06 

H3 

40  FIRST  LESSOXS  /.v  NUMB  EPS. 

LESSON  XIV. 

When  the  sum  of  a  column  equals  or  exceeds  10. 

1.  What  is  the  amount  of  §365,  $944,  and  $422? 

ANALYSIS. — i.  Write  the  numbers  one  un-    Slate  work. 
der  another,  units  under  units,  tens  under      $365 
tens,  etc.,  and  draw  a  line  underneath.  944 

2.  Add  the  figures  in  the  units'  column.        423 

The  sum  is  12  units,  equal  to  i  ten  and  2  units.     

Write  the  2  units  under  units'  place,  and  add    $1732  Am. 
the  i  ten  to  the  tens'  column,  because  it  is  of  the  same 
order. 

3.  The  sum  of  the  tens  is  13  tens,  equal  to  i  hundred 
and  3  tens.     Write  the  3  tens  under  tens'  place,  and  add 
the  i  hundred  to  the  hundreds'  column,  because  it  is  of  the 
same  order. 

4.  The  sum.  of  the  hundreds  is  17,  and  this  being  the 
last  column  we  set  down  the  whole  amount. 

Hence  the  sum  is  1732. 

NOTE. — At  first  give  examples  in  which  one  column 
amounts  to  ten,  or  more. 

2.  One  school  has  308  pupils,  another  96,  and 
another  435  :  how  many  have  all  ? 

3.  A  merchant  gained  $450  the  first  year,  $573 
the  second  year,  and  §695  the  third  year:  what 
was  the  whole  gain  ? 

4.  Find  the  sum  of  590  tons,  817  tons,  904 
tons,  and  1325  tons. 

5.  Three  men  sold  a  steamboat;  the  first  re- 
ceived 82125  as  his  share,  the  second  8936,  and  the 
third  $3688  :  what  was  the  value  of  the  steamboat? 


FIRST  LESSONS  IN  NUMBERS.  41 

6.  Add  508,  7009,  and  60,306. 

7.  A  captain  sold  his  vessel  for  $3425,  which 
was  $2050  less  than  cost:  what  did  it  cost  ? 

8.  A  man  gave  his  property  to  his  wife,  son, 
and  daughter;    to  his  daughter  1*3  gave  $3475, 
to  his  son  §5150,  and  to  his  wife  as  much  as  he 
gave  to  his  children :  what  was  the  value  of  his 
property  ? 

9.  A  grocer  bought  4  hogsheads  of  molasses; 
the  first  contained  95  gallons,  the  second  6  gal- 
lons more  than  the  first,  the  third  7  gallons  more 
than  the  second,  and  the  fourth  27  gallons  more 
than    the    third:    how    many    gallons    did    he 
purchase  ? 

RULE    FOR    ADDITION. 

1.  Write  the  numbers  one  under  another,  units 
under  units,  tens  under  tens,   hundreds  under 
hundreds,  etc. 

2.  Begin  at  the  right-hand  or  units'  column, 
and  add  each  column  separately. 

3.  When  the  sum  of  a  column  is  less  than  ten, 
write  it  under  the  column  added. 

4.  Where  the  sum  of  a  column  is  10,  or  more, 
write  the  units'  figure  under  the  column  added, 
and  add  the  remaining  figure  or  figures  to  the 
next  higher  order. 

5.  When  the  last  column  is  added,  set  down  the 
whole  amount. 

Proof. — Repetition  is  the  only  proof  of  addition. 


42  FIRST  LESSONS  IN  NUMBERS. 


SUBTRACTION. 


LESSON  I. 


Subtraction  is  the  process  of  finding  the  differ- 
ence between  two  numbers. 

The  Difference,  or  remainder,  is  the  number 
lef fc  after  subtracting. 

The  Minuend  is  the  number  from  which  the 
subtraction  is  made. 


FIRST  LESSONS  IN  NUMBERS.  43 

The  Subtrahend  is  the  number  to  be  subtracted. 

The  Sign  of  Subtraction  is  a  short  horizontal 
line  — ,  called  minus,  which  means  less. 

It  shows  that  the  number  on  the  right  is  to  be 
taken  from  the  number  on  the  left. 


LESSON  II. 

Principle. — Only  like  Numbers  can  be  subtracted. 

i  from  i  leaves  o.  i  from  6  leaves  5. 

i     "  2      "       i.  i  "      7      "      6. 

i     "  3      "       2.  i  "      8      "       7. 

i     "  4      "       3.  i  "      9      «       8. 

i     <•  5       "       4.  i  "    10      "       9. 

1.  Draw   3   chalk-lines    on    the   black-board ; 
erase  one  :  how  many  are  left  ? 

2.  Draw  4  lines  ;  erase   one :  how   many   are 
left? 

3.  John  had  5  cents  and  spent  one  cent  for  an 
apple  :  how  many  cents  had  he  left  ? 

Solution.— He  had  left  the  difference  between  1 
cent  and  5  cents,  which  is  four  cents. 
Copy  and  subtract  the  following  : 

(4.)   (5-)   (6.)   (7-)   (8.)     (90     (10.)   (n.)   (12.) 

123       4       3          678         9 
11111          11  11 


44  FIRST  LESSORS  IN  NUMBERS. 

LESSON  III. 

2  from  2  leaves  o.         2  from  7  leaves  5. 

2     "      3      "       i.         2     "      8       "       6. 

2        "         4          f;  2.  2        "         9          "'  7. 

2     "      5      "       3.         2     «    10       "       8. 

2        "          6          "          4.  2        "'    XI  4i          9. 

1.  Draw  three  lines  on  the  black-board  ;  erase 
two  :  how  many  are  left  ? 

2.  Place  four  books  in  a  row  ;  take  away  two : 
how  many  are  left  ? 

3.  Jane  bought  5  apples  and  ate  2 :  how  many 
had  she  left  ? 

Solution. — 2  apples  from  5  apples  leave  3  apples. 

4.  Joseph  earned  7  cents  ;  he  spent  two,  and 
saved  the  rest  :  how  many  did  he  save  ? 

5.  If  there  are  9  roses  in  a  bouquet,  and  Peter 
takes  out  two,  how  many  will  remain  ? 

6.  If  you  have  6  marbles  and  lose  2,  how  many 
have  you  left  ? 

7.  If  there  are   10  eggs  in  a  nest,  and  a  boy 
takes  out  two,  how  many  are  left  ? 

8.  A  hunter  saw  12  ducks  on  a  pond  ;  he  shot 
two  :  how  many  escaped  ? 

9.  Write  the  table  thus:  2  —  2=0. 

10.  What  number  is  two  less  than  n  ? 

(ii.)  (12.)  (13.)   (14.)  (15-)   (16.)  (i7-)  (18.) 

3        3        1        •'        6        78        9 


FIRST  LESSONS  IN  NUMBERS.  45 

LESSON  IV. 

3  from  3  leaves  o.        3  from  8  leaves  5. 

5  "  4  "  i.  3  k*  9  "  6. 
3  "  5  "  2.  3  "  10  "  7. 
3  -  6  "  3.  3  «  ii  "  8. 

3     "      7       "       4          3     "     12       «       9. 

1.  Charles  had  3  oranges  and  gave  one  to  each 
of  his  three  sisters  :  how  many  has  he  left  ? 

2.  John  had  4  birds,,  and  the  cat  killed  3  of 
them  :  how  many  were  left  ? 

3.  If  you  have  5  rabbits,  and  give  away  three, 
how  many  will  remain  ? 

4.  If  yon  had  6  cents,  and  spent  3,  how  many 
cents  will  you  have  left  ? 

5.  A  gentleman  built  7  houses  in  a  row ;  he 
sold  3  :  how  many  still  belong  to  him  ? 

6.  3  boys  out  of  9  were  promoted  :  how  many 
were  not  ? 

7.  Louise  bought  8  oranges  and  gave  away  3  : 
how  many  had  she  left  ? 

8.  A  carpenter  had   n   chisels,  and  broke  3  : 
how  many  remained  ? 

9.  Willie  had  ten   cents ;  he  bought  a  top'  for 
two  cents,  and  a  cord  for  i  cent :  how  much  had 
he  left  ? 

(10.)     (n.)     (12.)     (13.)     (14.)     (15.)     (16.) 
12         /-,'         14         15         16         17         18 


46  FIRST  LESSONS  IN  NUMBERS. 

LESSON  V. 

4  from  4  leaves  o.  4  from  9  leaves  5. 

4     ••       5       "       i.  4     "     10       "       6. 

4     •'•'       6       <•'        2.  4     ^     ii       "        7. 

4     "       7       "       3.  4     "     12       "       8. 

4     "      8       "       4.  4     «     13       -       9. 

1.  If  a  boy  had  4  cents,  and  bought  4  cents' 
worth  of  candy,  how  much  money  would  he  have 
left  ? 

2.  A  boy  bought  5  pencils  and  broke  4:  how 
many  has  he  left  ? 

3.  John  promised  to  make  6  kites  ;  he  has  4 
of  them  done :  how  many  more  must  he  make  ? 

4.  Edward  picked  7  quarts  of  berries,  and  sold 
4  quarts :  how  many  had  he  left  ? 

5.  George  caught  9  fish  and  his  brother  caught 
4:  how  many  did  George  catch  more  than  his 
brother  ? 

6.  A  hen   had    10  chickens;    four   died:  how 
many  are  still  alive  ? 

7.  A  farmer  had  12   sheep;    he  sold  3  and  i 
died  :  how  many  had  he  left  ? 

8.  A  box  of  crackers  weighed  13  pounds,  and  a 
box  of  candy  4  pounds  :  what  is  the  difference  in 
weight  ? 

(9.)         (10.)       (II.)        (12.)        (I3.)        (I4.)        (IS.) 

U         -4         .-J         26         27         28         20 


5 

leaves 

0. 

5  from 

10 

leaves 

5- 

6 

<• 

i. 

5 

t  k 

1  1 

*'* 

6. 

7 

(  .• 

2. 

5 

*• 

12 

•• 

7- 

8 

" 

3< 

5 

ft 

J3 

« 

8. 

9 

« 

4- 

5 

*•• 

14 

"'<•' 

9- 

er 

ic  had 

6 

rabbits, 

and 

sold   5  ; 

how 

FIRST  LESSORS  rx  NUMBERS. 

LESSON  VI. 

5  from 

5  " 
5  « 
5  " 
5  " 

1.  Fred 

many  had  he  left  ? 

2.  If  he  has  i  left,  how  many  must  he  buy  so 
as  to  have  8  rabbits  ? 

3.  A  pail  filled  with  water  weighed  9  pounds  ; 
without    the  water    it  weighed  4  pounds  :  how 
many  pounds  did  the  Avater  weigh  ? 

4.  A   merchant    paid    n    cents   a   pound    for 
sugar  and  sold  it  for  5  cents  a  pound :  what  was 
the  loss  on  each  pound  ? 

5.  A  carpenter  earned  $12,  and  spent  $5* for  a 
saw:  how  many  dollars  had  he  left  ? 

6.  A  grocer  paid  5  cents  a  pound  for  cheese, 
and  sold  it  for  13  cents :  what  was  the  gain  ? 

7.  John  had  $14,  and  he  spent  $5  for  a  hat: 
how  many  dollars  had  he  left  ? 

8.  William  is  14  years  old,  and  his  sister  is  5 
years  younger:  how  old  is  his  sister  ? 

(9.)    (10.)     (ii.)     (12.)     (13.)    (14.)     (15.)    (16.) 

21        22        23        24.        25        26        27        28 

ft          -5          5          5          5555 


48  FIRST  LESSORS  ix  NUMBERS. 

LESSON  VII. 

6  from  6  leaves  o.  6  from  1 1  leaves  5. 

6     "      7      "       i.  6     "  12       <•  6. 

6     ••'      8      "       2.  6     V*  13      "  7. 

6     "      9       "       3.  6     "  14       "  8. 

6     **     10       <•'       4.  6     •*  15       ••  9. 

1.  Jane  carried  7  quarts  of  berries  to  market, 
and  sold  6 :  how  many  quarts  were  left  ? 

2.  Charles  rises  at  6  o'clock,  and  studies  till  8 : 
how  many  hours  does  he  devote  to  study  ? 

3.  If  you  pay  6  cents  for  an  orange,  and  sell  it 
for  9  cents,  how  much  will  you  gain  ? 

4.  If  a  grocer  pays  §10  a  barrel  for  flour,  and 
sells  it  for  $6,  how  much  will  he  lose  ? 

5.  There  were   n  chairs  in  a  room,  and  Mary 
removed  6  :  how  many  were  left  ? 

6.  -If  you  had  12  cents,  and  spent  4  for  cake 
and  2  for  apples,  how  many  cents  will  remain  ? 

7.  6  and  how  many  make  14  ?    Why  ? 

8.  13  is  the  minuend,  and  6  is  the  subtrahend: 
what  is  the  remainder  ? 

9.  A  farmer  owned  15  sheep,  but  a  wolf  killed 
six:  how  many  were  left  ? 

10.  6  and  how  many  will  make  20  ? 

(ii.)  (12.)   (13.)   (4.)  (15.)   (16.)   (17.)   (18.)- 

27 


FIRST  LESSONS  IN  NVMBBX&          49 
LESSON   VIII. 

7  from  7  leaves  o.  7  from  12  leaves  5. 

7     "      8       "      i.  7     "      13  "       6. 

7     "      9       "      2.  7     "      14  "       7. 

7     "     10       "      3.  7     "      15  "       8. 

7     "    ii       "4.  7     "      16  "       9. 

1 .  A  traveller  started  in  the  7  o'clock  train  and 
reached  home  at  9 :  how  long  was  he  in  the  cars  ? 

2.  Frank  passes  10  barns  on  his  way  to  school ; 
7  are  old :  how  many  are  new  ? 

3.  There  were  n  chickens  in  a  brood,  and  the 
rats  killed  all  but  7  :  how  many  were  killed  ? 

4.  Tom  is  now  twelve  years  old,  and  he  has 
been  to  school  7  years :  how  old  was  he  when  he 
began  to  go  to  school  ? 

5.  If  I  earn  13  cents  and  spend  7,  how  many 
cents  will  I  have  left  ? 

6.  A  dress  cost  $14  and  a  hat  cost  $6  less  :  what 
was  the  cost  of  ihe  hat  ? 

7.  There  were  15  children  in  the  park,  but  7 
have  gone  home  :  how  many  remain  ? 

8.  Jane  is  16  years  old,  and  Louise  is  7  years 
younger  :  how  old  is  Louise  ? 

9.  What  is  the  difference  between  7  and  17  ? 

(10.)     (n.)     (12.)     (13.)     (14.)     (IS-)     (16.) 
80         32         34         35         36         38         39 

7          7          7-         7          7  7          7 


50  FIRST 

LESSON  IX. 

8  from  8  leaves  o.  8  from  13  leaves  5. 

8     "      9       "      i.  8  «      14  "       6. 

8     "    10       "      2.  S  "      15  "       7. 

8     "    ii       "      5  8  "      16  "       8. 

8     ^    12       "      4.  8  "      17  "       9. 

1 .  A  farmer  paid  $8  dollars  a  barrel  for  flour 
and  sold  it  for  $9  :  how  much  did  he  gain  ? 

2.  What  is  the  difference  between  $8  and  $10  ? 

3.  ii  passengers  were  riding  in  a  cat  :  S  got 
out :  how  many  continued  to  ride  ? 

4.  .What  mv  aw  from  a  1 2-foot 
board  to  make  it  8  feet  long  ? 

5.  Charles  is  8  years  old ;  how  many  years  will 
pass  before  he  will  be  13  ? 

6.  Francis  saw  14  ducks  on  a  lake,  and  shot  5 : 
how  many  escaped  ? 

7.  If  William  has  $8  and  can  save  $i  a  day: 
how  long  must  he  work  to  have  $15  ? 

8.  A  sloop  sailed  8  miles  in  an  hour,  and  a 
steamer  16  miles :  how  far  were  they  apart  at  the 
end  of  the  first  hour  ? 

9.  Two  men  paid  $17  for  a  boat ;  one  agreed  to 
pay  $8 :  what  must  the  second  ma 

(10.)   (II.)   (12.)   (I3.)    (I4.)   (150    06.)    (I 

31      32      S3  -?       37 

S         S         S         S         S         S         S         S 


FIRST  LESSONS  ix  NUMBERS.  51 

LESSON   X. 

9  from  9  leaves  o.  9  from  14  leaves  5. 
9  "  10  "  i.  9  4*  1S  6i  6. 
9  "'•'  ii  "  2.  9  "  1 6  "  7. 
9  "  12  -  3.  9  "  17  W  8. 
9  ?  13  K  4-  9  "  l8  "  9- 

1.  Harry  bought  a  knife  for  10  cents  and  sold 
it  for  9  cents  :  how  many  cents  did  he  lose  ? 

2.  Charles  borrowed  n  cents  and  paid  back  9, 
how  many  does  he  still  owe  ? 

3.  A  farmer  planted  12  pear-trees,   and  9  of 
them  bear  fruit :  how  many  do  not  ? 

4.  A  grocer  paid  9  cents  a  pound  for  cheese 
and  sold  it  for  13  cents :  what  did  he  gain  on  each 
pound  ? 

5.  School  opens  at  9  o'clock  :  how  many  hours 
till  noon  ? 

•   6.  A  scholar  answered  9  questions  out  of  14 : 
how  many  did  he  miss  ? 

7.  James  saved  15  cents  ;  he  bought  a  copy- 
book for  8  cents,  and  a  pen  for  i  cent :  how  much 
had  he  left  ? 

8.  A  boy  had  16  marbles  and  won  4;  then  he 
lost  9  :  how  many  had  he  left  ? 

(9.)    (10.)    (n.)    (12.)    (13.)    (14.)     (150   (16.) 

9         19       29        30       32        34        36        38 
9          9999999 


FufST  LESSOXS  IN  Xm 
LESSON  XL 


To  subtract  when  each  figure  in  the  subtra- 
hend is  less  than  the  one  above  it. 

i.  Find  the  difference  between  75  and  21. 

ANALYSIS.  —  i.  Write  the  less  number  un-    Slate  wwk. 
der  the  greater,  units  under  units,  tens  under          75 
tens,  etc.,  and  draw  a  line  underneath.  21 

2.  Subtract  the  units  thus  :  i  unit  from  5 

units  leaves  4  units.     Write  the  remainder          54  Ans. 
under  the  units'  place,  because  it  is  units. 

3.  Subtract  the  tens,  and  write  the  remainder  under  the 
tens'  place,  because  it  is  tens. 

Hence  the  remainder  is  54. 


(*•)          (3-)             (4-)              (S-) 
From  59           74             295             359 
Take  27          31            134            214 

(7-)                 (8.)                 (9.) 
From  176  pounds.  346  sheep.     569  horses. 
Take   162        *'•        313      '*        266      '• 

(6.) 
842 
521 

(10.) 

138 

(II.)                    (12.)                       (I3.) 

From  694  men.     359  miles.      189  tons. 
Take  684     "         45      "          72      " 

(HO 
$394 
103 

(150                  (16.)              (17.) 
From     468  barrels.     963  trees.     277  feefc. 
Take       57       "            32     «          64    « 

(18.) 

$543 
241 

Fiitsr  LESSOXS  ix  NUMBERS.  5;i 

LESSON  XII. 

When  a  figure  in  the  subtrahend  is  greater 
than  the  orie  above  it. 

1.  What  is  the  difference  between  575  and  327? 
ANALYSIS.— i.  Write  the  less  num-  Slate  work. 

ber  under  the  greater,  units  under  «  IB 

units,   tens  under   tens,   etc.,    and  5  "^N^ 

draw  a  line  underneath.  327 

2.  Seven  units  from  5  units  can- 
not be  taken  ;    we  must  take  one  248  Am. 
ten  from  the  ten's  figure  and  add  it  to  the  5  units,  which 
makes  15  units.     7  units  from  15  units  leave  8  units,  which 
we  write  under  units'  place,  because  it  is  units. 

3.  Since  we  took  i  ten  from  the  7  tens,  there  are  6  tens 
left ;  and  2  tens  from  6  tens  leave  4  tens,  which  we  write 
under  tens'  place,  because  it  is  tens. 

4.  Three  hundreds  from  5  hundreds  leave  2  hundreds. 
Hence  the  remainder  is  248. 

NOTE. — i.  Take  one  from  the  next  figure  :  do  not  bor- 
row and  pay  back. 

2.  It  is  necessary  at  first  to  mark  this  change  in  the 
slate  work.  In  review,  however,  insist  on  a  dot  being 
placed  over  the  figure  from  which  i  is  taken  (575). 

2.  I  sold  a  watch  for  $i  10  which  cost  $75  :  what 
was  the  gain  ? 

3.  If  I  pay  35  cents  for  a  brush,  how  much 
change  will  I  receive  out  of  a  $2  bill  ? 

4.  A  farmer  sold  a  horse  for  $75,  and  bought  a 
cow  for  $35  and  a  calf  for  $15:  how  many  dol- 
lars had  he  left  ? 

5.  A  gentleman  planed  $1250  in  bank  ;  lie  drew 


54  FIRST  Lf:sso.\'fi  /.v 


out  at  one  time  $360,  and  at  another  $237  :  what 
sum  remains  in  bank  ? 

6.  I  purchased  a  house  for  $'18572,  and  sold  it 
for  $20000  :  what  did  I  gain  ? 

ANALYSIS.  —  i.  Two  units  from  o  unit  State  work. 
cannot  be  taken.  We  must  take  one  iVS^X^io 
from  the  next  significant  figure.  ^X.o  o  o  o 

2.  i  ten  thousand  from  2  ten  thou-     18572 
sands    added   to  the  thousands  makes     - 


10  thousands,  leaving  i  ten  thousand.  0  i  4  2 
i  thousand  from  10  thousand  added  to  the  hundreds 
makes  10  hundreds,  leaving  9  thousands,  i  hundred 
from  10  hundreds  added  to  the  tens  makes  10  tens, 
leaving  9  hundreds,  i  ten  from  10  tens  added  to  the 
units  makes  10  units,  leaving  9  tens. 

3.  2  units  from  10  units  leave  8  units.  7  tens  from  9 
tens  leave  2  tens.  5  hundreds  from  9  hundreds  leave  4 
hundreds,  etc.  Hence  the  gain  is  $1428. 

RULE    FOR   SUBTRACTION". 

1.  Write   the  less   number   wider  the  greater, 
units  under  units,  tens  under  tens,  etc. 

2.  Begin  at  the  right  or  units'  place,  and  sub- 
tract each  figure  of  the  longer  number  from   the 
one   above    it,   setting   the   remainder   under   the 
column  subtracted. 

3.  If  the  lower  figure  Is  greater  than  the  upper 
figure,  increase  the  latter  by  ten,  and  consider  the 
next  higher  figure  one  less  ;  then  subtract. 

Proof.  —  The  sum  of  the  remainder  and  subtra- 
hend should  equal  the  minuend. 


FTI?ST  .LKHHOXS  r.v  Nr 


MULTIPLICATION. 


LESSON  I. 

Multiplication  is  the  process  of  taking  one  of 
two  numbers  as  many  times  as  there  are  units  in 
the  other. 

The  Multiplicand  is  the  number  to  be  multi- 
plied. 

The  Multiplier  is  the  number  which  shows  how 
many  times  the  multiplicand  is  to  be  taken. 


r>fi  FIRST  LFSSOXS  rx 


The  Product  is  the  result  obtained. 
The  Sign  of  multiplication  is  an  oblique  cross 
X-     It  is  read  multiplied  by.  or  times. 


LESSON    II. 

Principles. — 1.  The  multiplier  is  an  abstract 
number.  2.  The  multiplicand  and  product  are 
like  numbers. 

2  times  i  are   2.  2  times  7  are  14. 

2         "          2       "       4.  2         "         8      **        1 6. 

2      "       3    "     6.  2      "      9    "     18. 

2         "          4       "       8.  2          {;      10      "       20. 

2         "' ''  5       *  *     I O.  2          * k       I  I       '•        22. 

2         "•  6       "     12.  2          *"       12       "        24. 

1.  Draw  a  line  on  the  black-board  each  time 
that  I  give  the  signal.      When  two  lines  were 
drawn,  how  many  times  was  the  signal  given  ? 

2.  Two  times  one  line  are  how  many  ? 

3.  What  is  the  cost  of  2  apples  at  5  cents  each  ? 
Solution. — Since  1  apple  cost  5  cents,  2  apples 

will  cost  2  times  5  cents,  which  are  ten  cents. 

4.  If  you  can  hold  8   chestnuts  in  one  hand. 
how  many  can  you  hold  in  both  ? 

5.  Each  boy  has  ten   fingers  :  how  many  fin- 
£ers  have  two  bovs  ? 


FTKST  LESSONS  IN  N 
LESSON    III. 


3  times  i  are  3.  3  times  7  are  21. 

3      ff      2    "     6.  3      "     8     "    24. 

3      "      3    "     9-  3      "      9     "    27- 

3      "     4    "  12.  3      "    10     "    30. 

3      "      5    "  J5-  3      "    IJ     "    33- 

3      «      6    «  18.  3      "    12     «    36. 

1.  One  ox  has  2  horns  :  how  many  horns  have 
3  oxen  ? 

2.  In  each  of  3  beats  there  are  3  men  :  how 
many  are  there  in  all  ? 

3.  How  many  feet  are  in  4  yards  ? 

4.  A  truckman  can  carry  6  barrels  at  a  load  : 
how  many  barrels  can  he  take  in  3  loads  ? 

5.  Mary  is  7  years  old,  and  her  brother  is  3 
times  as  old :  what  is  the  age  of  her  brother  ? 

6.  When  pine-apples  are  8  cents  each,    what 
will  3  pine-apples  cost  ? 

7.  At  $10   each    what  will   be  the  price  of  3 
stoves  ? 

8.  What   will   3  yards  of   muslin  cost    at    n 
cents  per  yard  ? 

9.  If  a  copy-book  contains     12    leaves,    how 
many  leaves  will  3  copy-books  contain  ? 

Write  the  table,  thus : 

(A)  3x1=3.  (B)  1x3=3. 

3x2=6.  2x3=0. 

3x3=9.  3x3=9. 


58          FIRST  LESSONS  IN  NUMBERS. 

LESSON   IV. 

4  times  i  are    4.  4  times    7  are  28. 

4      "      2     "      8.  4      "        8     "    32. 

4      "      3     "    12.  4      "        9     "    3<5. 

4   .  "      4     "     1 6.  4      "       10     "    40. 

4      "      5     "    20.  4      "       ii     "    44- 

4      "      6    "    24.  4      "       12     "    48. 

1.  What  will  4  yards  of  silk  cost  at  $7  a  yard  ? 

2.  If  a  boy  works  5  hours  each  day,  how  many 
hours  does  he  work  in  4  days  ? 

3.  How  many  feet  have  3  dogs  ? 

4.  There  are  4  gills  in  one  pint:  how  many 
gills  in  6  pints  ? 

5.  If  one  table  cost  $7,  what  will  4  tables  cost  ? 

6.  If  one  pound  of  sugar  cost  8  cents,,  how 
many  cents  will  4  pounds  cost  ? 

7.  I  have  4  boards,  each  9  feet  long :  what  is 
the  united  length  of  the  boards  ? 

8.  Bought  4  pounds  of  sugar  at   10  cents  a 
pound,  and  sold  it  at  12  cents  a  pound  ;  what  did 
I  gain  ? 

9.  At  the  rate  of  7  for  a  cent,  how  many  mar- 
bles can  be  bought  for  4  cents  ? 

10.  In  form  A,  which  is  the  multiplier  ? 

11.  In  form  B,  which  is  the  multiplier  ? 

12.  Write  the  table  in  both  forms. 

(13.)  (14.)  (15.)  (16.)  (17.)  (18.)  (19.) 
Multiply  5  9  11  8  12  21  ..'.> 
By  «.  -.£  33  4  4  4 


LESSONS  IN  NUMBERS.  59 

LESSON  V. 

5  times  i  arc   5.  5  times  7  are   35. 

5      "      2    "    10.  5      "      8    «     40.       ' 

5      "      3    "    15-  5      "     9    "     45- 

5      "      4    (i   20.  5      "    10    "     50. 

5      ki      5    "    25.  5      "    ii    "     55. 

5      "     6    "   30.  5      "    12    "     60. 

1.  What  will  be  the  cost  of  5  hats  at  $2  each  ? 

2.  At  3  cents  each,  what  will  be  the  cost  of 
three  oranges  ? 

3.  Frank  lives  2  miles  from  school :  how  many 
miles  does  he  walk  in  5  days  ?    Ans.  20  miles. 

4.  If  a  man  earns  $4  a  day,  how  many  dollars 
will  he  earn  in  5  days  ? 

5.  If  6  marbles  can  be  bought  for  one  cent, 
how  many  can  be  bought  for  5  cents  ? 

6.  There  are   7   days  in  i  week :  how  many 
days  are  there  in  5  weeks  ? 

7.  Ten  cents  make  one  dime :  how  many  cents 
in  5  dimes  ? 

8.  "What  will   11   quarts  of  chestnuts  cost  at 
5  cents  a  quart  ? 

9.  How  many  inches  in  5  feet  ?    In  4  feet  ? 

10.  How  many  fives  make  20  ?  etc. 

11.  Write  the  table  in  both  forms. 

(12.)  (13.)  (14.)  (15.)  (16.)  (17.) 
Multiply  11  12  21  27  31  111 
By  555555 


FIRST  LESSONS  IN  XUMBE. 

LESSON 

V 

[Jl 

6 
6 

times  i  are   6. 

2       "  :      12. 

6 
6 

times  7 
*'     8 

6 
6 
6 
6 

"      3    "    18. 

-    "      4     "    24. 

"     5    "   3°- 
«     6    -    36. 

6 
6 
6 
6 

"      9 

"    10 

"    ii 

"     12 

GO 


are   42. 

"  48. 
"  .54- 
"  60. 
"  66. 

"        72. 

1.  A  workman  earned  $2  a  day:  how  many 
dollars  did  he  earn  in  6  days  ? 

2.  Sarah  saved  $3  each  month  :  how  many  dol- 
lars had  she  at  the  end  of  6  months  ? 

3.  A  grocer  paid  $5  a  barrel  for  flour,  and  sold 
it  for  89 :  what  did  he  gain  on  6  barrels  ? 

4.  A  carpenter  built  6  fences,  each  fence  having 
5  posts :  how  many  posts  did  he  use  ? 

5.  He  built  6  houses,  each  house  having  6  win- 
dows :  how  many  window-frames  were  required  ? 

6.  If  one  sheet  of  paper  makes  8  leaves  of  a 
copy-book,  how  many  leaves  will  6  sheets  make  ? 

7.  A  gentleman  hired  5  workmen  at  $2  a  day  : 
how  much  must  he  pay  them  for  6  days'  work  ? 

8.  A  farmer  carried  6  dozen  of  eggs  to  mar- 
ket, and  sold  them  for  i  cent  apiece :  what  did 
he  get  for  them  ? 

(9.)  (10.)  (n.)  (12.)  (13.)  (14.) 
Multiply  .9  11  21  111  201  311 
Bv  '>  6  6  6  6  6 


FIRST  LESSONS  IN  NUMBERS.  61 

LESSON  VII. 

7  times  i  are     7.  7  times  7  are  49. 

7      "      2  "     14.  7      "  8    "  56. 

7      -'      3  "     21.  7      "  9    «  63. 

7       *'•'      4  *•     28.  7      **  10    *•'  70. 

7       "'      5    "     35-  7      "      ii    "     77- 

7      M      6    "     42.  7      "      12    <f     84. 

1.  A  jeweller  paid   $3  apiece  for  rings,    and 
sold  them  for  $4  :  what  did  he  gain  on  7  rings  ? 

2.  Each  room  in  a  hotel  is  lighted  by  2  gas- 
jets  :  how  many  jets  are  in  7  rooms  ? 

3.  How    many  horseshoes  will   a  blacksmith 
use  in  shoeing    7  horses  ? 

4.  If  a  barrel  will  hold  3  bushels  of  apples, 
how  many  bushels  will  7  barrels  hold  ? 

5.  What  will  7  pairs  of  boots  cost  at  $5  a  pair  ? 

6.  How  many  feet  in  7  boards  each  6  feet  long? 

7.  How  many  days  are  there  in  7  weeks  ? 

8.  Alice  is  8  years  old,  and  her  father  is  7  times 
as  old  as  she  is :  what  is  her  father's  age  ? 

9.  7  tens  are  how  many  units  ? 

10.  If  a  family  use  n  pounds  of  sugar  in  one 
week,  how  many  pounds  will  they  use  in  7  weeks  ? 

11.  What  will  be  the  price  of  a  dozen  spools  of 
cotton  at  7  cents  a  spool  ? 

(12.)  (13.)  (14.)  (15.)  (16.)  (17-) 
Multiply  11  9  101  201  211  311 
BY  777  7  7  7 


6x5  FIRST  LESKOXS  ix 

LESSON    A 


8  times  i  are  S.  8  times  7  are  56. 

8     "       2  k*    16.  8  *'4'       8  "  64. 

8     "       3  "    24.  8  "       9  "  72. 

8     "       4  "    32.  8  "      10  "  80. 

8^5  "   40.  8  "      ii  "  88. 

8     "       6  "   48.  8  "      12  "  96. 

1.  8  quarts  make  a  peck  :  how  many  quarts  in 
8  pecks  ? 

2.  What  will  be  the  cost  of  8  yards  of  muslin, 
at  4  cents  a  yard  ? 

3.  Five  boards,  each  8  feet  long,  reach  from  the 
door  of  a  cottage  to  the  gate  :  what  is  the  length 
of  the  yard  ? 

4.  An  agent  rented  a  house  at  §7   a  month  : 
how  much  did  he  receive  in  8  months  ? 

5.  A  carpenter  made   8  ladders,   each  having 
12  rungs  :  how  many  rungs  did  he  use  ? 

6.  What  will  a  boy  receive  for  8  quarts  of  ber- 
ries at  9  cents  a  quart  ? 

7.  At  10  cents  each  what  will  8  oranges  cost  ? 

8.  8  times  1  1  miles  are  how  many  miles  ? 

9.  What  will  a  dozen  copy-books    cost   at   8 
cents  each  ? 

(10.)   (n.)  (12.)  (i3.)    (i4:)   (i5.) 

9  11  7         101         111         210 

<S*  S  8  8  8  8 


FIRST  LESSORS  IN  NUMBERS.  63 

LESSON  IX, 

9  times  i  are     9.  9  times  7  are  63. 

9  "      2    "    1 8.  9      "  8    "     72. 

9  "      3    "    27.  9      "  9    "     81. 

9  "      4    "    36.  9       "  10    "     90. 

9      "      5     "    45-  9      "      ii    rt     99- 

9      "      6    "    54.  9      "      12    "  1 08. 

1.  Sold  9  barrels  of  flour  at  a  profit  of  $2  a 
barrel :  what  did  I  gain  ? 

2.  A  carriage-maker  finished  9  carriages :  how 
many  wheels  did  he  use  ? 

3.  How  many  shelves  can  be  made  out  of  9 
boards,  if  one  board  will  make  three  shelves  ? 

4.  What  is  the  cost  of  9  tables  at  $5  each  ? 

5.  Paid  5  cents  each  for  pears,  and  sold  them  at 
a  gain  of  i  cent  :  what  were  9  pears  sold  for  ? 

6.  What  will  9  yards  of  velvet  cost  at  $7  a  yd.  ? 

7.  Each  of  9  boys  answered  8  questions  ;  how 
many  questions  were  answered  ? 

8.  9  times  naught  are  how  many  ? 

9.  Bought  9  yards  of  muslin  at  n  cents  a  yard: 
how  much  change  did  I  receive  out  of  a  dollar  ? 

10.  What  will  9  calves  cost  at  $12  each  ? 

11.  Write  the  table  in  both  forms. 

(12.)  (13.)  (14.)  (15.)  (16.)  (17.) 
7  9  11  1001  1010  2001 
9  0  9  9  9  9 


G4  FIRST  LESSONS  AV  Nui 

LESSON  X. 
10  times  i  are  10.        10  times     7  are     70. 


IO 

f  (    2 

a 

20. 

10    " 

8  " 

80. 

IO 

"   3 

ft 

3°- 

IO    " 

9  " 

90. 

IO 

"   4 

a 

40. 

IO    " 

10   " 

IOO. 

IO 

"   5 

ti 

5°- 

IO    " 

n  (i 

IIO. 

IO 

"   6 

a 

60. 

10    " 

12  " 

120. 

LESSON  XL 


n  times    i  are    n. 

II        "  2 

ii     "        3 


n 
n 
n 


4 

5 
6 


II. 

n 

times    7 

are    77. 

22. 

n 

8 

"     88. 

33- 

n 

"       9 

'•      9°- 

44. 

n 

I  O 

"      IIO. 

55- 

n 

n 

"      121. 

66. 

n 

"        12 

X    i32- 

LESSON   XII. 


12  times  i  are  12. 

12        ff  2     "  24. 

12        «  3     «  36. 

12        fi  4    "  48. 

12        "  5     "  60. 

12     •'•'  6   *•'  72. 


12  times    7  are    84. 

12     "        8  "      96. 

12  "  C)  "  1 08. 

12  "  10  fi  120. 

12  ig  II  itf  132. 

12  "  12  •'  144. 


FIRST  LESSONS  IN  NUMBERS.  65 

LESSON  XIII. 

To  multiply  by  one  figure  when  the  partial 
products  are  less  than  10. 

i.  What  will  3  houses  cost  at  $1213  each  ? 
ANALYSIS. — i.  Write  the  multiplier  under    Slate  work. 
the  right-hand  figure  of  the  multiplicand.  $1213 

2.  Multiply  the  units  figure  of  the  multi-             3 
plicand  by  the  multiplier.     3  times  3  units 

are  9  units  ;    which  we  write  under  units'      $3639  Ans. 
place,  because  it  is  units. 

3.  3  times  i  ten  are  3  tens  ;  which  we  write  under  tens' 
place,  because  it  is  tens. 

Continue  thus  until  each  figure  of  the  multiplicand  has 
been  multiplied.  Hence  the  product  is  $3639. 

NOTE. — Show  that  multiplication  is  a  short  method  of 
adding  equal  numbers. 


When  a  partial  product  is  10,  or  more, 

What  will  5  carriages  cost  at  $417  each  ? 

ANALYSIS. — i.  Write  the  multiplier  under    Slate  work. 
the  right-hand  figure  of  the  multiplicand.        $417 
Begin  at  units'  place  to  multiply.  5 

2.  5  times  the  7  units  are  35  units,  equal 

to  3  tens  and  5  units.  Write  the  5  units  $2085  Ans. 
under  the  figure  multiplied,  and  add  the  3  tens  to  the  pro- 
duct of  the  tens. 

3.  5  times  i  ten  are  five  tens,  and  3  tens  make  8  tens. 
Write  the  8  under  the  figure  multiplied. 

4.  5  times  4  hundreds  are  20  hundreds  :  this  being  the 
last  figure  to  be  multiplied,  we  set  down  the  whole  amount. 

NOTE.— Teach  multiplication  by  10,  n,  arid  12  by  one 
operation. 


66  FIRST  LESSORS  AV  S  UMBERS. 

LESSON  XIV. 

When  the  multiplier  is  more  than  12. 

What  will  24  pianos  cost  at  $638  each  ? 

ANALYSIS.— i.  Write  the  multiplier  under    Slate  work. 
the  multiplicand,   units  under  units,  tens        $638 
under  tens,  etc.  24 

2.  4  times  8  units  are  32  units,  or  3  tens        

and  2  units.     Write  the  2  units  under  the        2552 
figure  multiplied,  and  add  the  3  tens  to  the      1276 
product  of  the  tens.  

3.  4  times  3  tens  are  12  tens,  and  3  tens    $15312  Ans. 
are  15  tens,  or  i  hundred  and  5  tens.  Write  the  tens  in  tens' 
place,  and  add  the  hundreds  to  the  product  of  the  hundreds. 

4.  Continue  thus  until  each  figure  of  the  multiplicand 
has  been  multiplied  by  the  units  figure  of  the  multiplier. 

5.  2  tens  times  8  units"  are  16  tens,  or  i  hundred  and  6 
tens.    Write  the  tens  under  the  figure  multiplied  by,  and 
add  the  i  hundred  to  the  next  product. 

6.  2  tens  times  3  tens  are  6  hundreds,  and  i  hundred 
are  7  hundreds.    Write  the  7  in  hundreds'  place,  etc. 

7.  Add  the  partial  products. 

RULE    TOR    MULTIPLICATION. 

i.  Write  the  multiplier  under  the  multiplicand, 
units  under  units,  etc. 

2.'  Multiply  the  multiplicand  by  each  figure  of 
the  multiplier,  and  set  the  first  figure  of  each 
partial  product  under  the  figure  multiplied  by. 

3.  Add  the  partial  product*. 

Proof. — Repetition  is  the  only  proof  of  multipli- 
cation until  division  has  been  taught. 


LESSONS  rx  LUMBERS. 


67 


DIVISION. 


LESSON   I. 

Division  is  the  process  of  finding  how  many 
times  one  number  is  contained  in  another. 

Or,  Division  is  the  process  of  finding  one  of 
the  equal  parts  of  a  number. 

The  Dividend  is  the  number  to  be  divided. 

The  Divisor  is  the  number  to  divide  by. 

The  Quotient  shows  how  many  times  the  divisor 
is  contained  in  the  dividend. 


68         .  FIRST  LESSONS  ix  NUMBERS. 

The  Remainder  is  the  part  of  the  dividend  left 
over  when  the  division  is  not  exact.  It  is  always 
less  than  the  divisor.  When  there  is  no  remain- 
der the  division  is  said  to  be  exact. 

The  Sign  of  Division  is  a  short  horizontal  line 
between  two  dots  -*-.  It  is  read  divided  by. 

Placed  between  two  numbers,  it  shows  that  the 
one  on  the  left  is  to  be  divided  by  the  one  on  the 
right. 


LESSOR.  II. 
2  in    2,     i  time.          2  in  12,     6  times. 


2, 

i 

time. 

2 

in 

12, 

6 

4, 

2 

times. 

2 

(t 

14, 

7 

6, 

3 

<e 

2 

« 

16, 

8 

8, 

4 

{( 

2 

(( 

18, 

9 

10, 

5 

ft 

2 

ef 

20, 

10 

1.  How  many  times  2  horses  are  12  horses  ? 

2.  How  many  apples  at  2  cents  each  can  you 
buy  for  4  cents  ? 

Solution.  —  You  can  buy  as  many  apples  for  4 
cents  as  2  cents,  the  price  of  one  apple,  is  con- 
tained times  in  4  cents,  which  is  2  times  ;  there- 
fore, 2  apples  can  be  bought. 

3.  How  many  peaches  at  2  cents  each  can  yon 
buy  for  6  cents  ? 

4.  How  many  $2  bills  make  twenty  dollars  ? 

5.  If  2  dresses  cost  §18,  what  will  i  dress  cost  ? 


FTRST  LESSONS  ix  NUMBERS.  69 

LESSON    III. 

3  in  3,  i  time.  3  in  1 8,  6  times. 

3  "  6,  2  times.  3  "    21,  7      " 

3  "  9,  3      "  3  "    24,  8     '« 

3  «  12,  4      "  3  v<    27,  9     •« 

3  "    J5>     5      "  3  "    3°?   I0      " 

1.  How  many  kites  at  3  cents  each  can  you 
buy  for  6  cents  ? 

2.  3  feet  make  a  yard  :  how  many  yards  are 
there  in  9  feet  ? 

3.  If  one  boat  holds  3  boys,  how  many  boats 
will  be  required  for  12  boys  ? 

4.  If  you  can  buy  a  ring  f qr  3  cents,  how  many 
can  you  buy  for  15  cents  ? 

5.  A  kite-frame  requires  3  sticks :  how  many 
kites  can  be  made  with  18  sticks  ? 

6.  A  plate  holds  3  apples:  how  many  places 
will  be  required  for  2 1  apples  ? 

7.  How  many  bags  will  be  required  to  hold  24 
bushels  of  potatoes,  if  one  bag  holds  3  bushels  ? 

8.  How  many  times  3  cents  are  27  cents  ? 

9.  30  is  how  many  times  3  ? 

10.  How  many  threes  in  15  ? 

11.  3  is  contained  in  21  how  many  times  ? 

12.  Continue:  3+3=1.     6+3=2.     9+3=3. 

(13.)        (14.)        (15.)         (16.)        (17.)        (18.) 
3)6         3)12         3)15         3)18         3)2 4         3)30 


70  FIRST  LESSOXS  i.\  XC 

LESSOX  IV. 


4  in    4>  i  time.  4  in  24,     6  times. 

4  "     8,  2  times.  4  "  28,     7      " 

4  "    12,  3       "  4  «  32,     8       « 

4  "    16,  4      "  4  '"  36,     9       ". 

4  "    20,  5       ?f  4  "  40,.  10       « 

1.  If  4  hats  cost  $8,  what  will  one  hat  cost  ? 
Solution.—  If  4  hats  cost  $8,  one  hat  will  cost 

one-fourth  of  $8,  which  is  2  dollars. 

2.  If  4  yards  of  silk  cost  12  dollars,  what  will 
one  yard  cost  ? 

3.  If  4  copy-books  cost  16  cents,  what  will  one 
copy-book  cost  ? 

4.  If  4  panes  of  glass  cost  20  cents,  what  will 
one  pane  cost  ? 

5.  If  4  wheels  are  needed  for  one  carriage,  how 
many  carriages  will  24  wheels  supply  ? 

6.  If  one  bench  will  seat  4  boys,  how  many 
benches  will  seat  28  boys  ? 

7.  How  many  dresses  will  32  yards  of  ribbon 
trim,  if  it  takes  4  yards  to  trim  one  dress  ? 

8.  If  4  boys  earn  40  cents,  what  will  be  each 
boy's  share  ? 

9.  Continue:  4+4=*-     8+4=2-     12+4=3. 

(10.)       (ii.)       (12.)      (13.)       (14.)     (15.) 
4)8      4)1*     4)20     4)32     4)40     4)44 


FIRST  LESSOXS  ix  NVMBEKX.          71 
LESSON  V. 


5  in     5,   i  time. 

5  in  30,     6  times. 

5  "    10,  2  times. 

5  ^    35,     7      " 

5  "    '5,  3      " 

5  "    4o,     8      " 

5   "    2o,  4       " 

5   ik'    45?     9      " 

5  "    25,  5      " 

5   "    50,   10      " 

1.  How  many  fans  at  5  c6nts  eacli  can  you  buy 
for  5  cents  ? 

2.  How  many  spools  of  thread  at  5  cents  each 
can  be  bought  for  10  cents  ? 

3.  How  many  times  can  5  cents  be  taken  from 
15  cents  ? 

4.  If  the  railroad  fare  is  5  cents  a  mile,  how  far 
can  you  ride  for  20  cents  ? 

5.  If  you  pay  $5  apiece  for  sheep,  how  many 
sheep  can  you  buy  for  $25  ? 

6.  An  orchard  contains  30  trees,  and  has  5  trees 
in  each  row  :  how  many  rows  in  the  orchard  ? 

7.  How  many  fives  in  35  ? 

8.  How    many    bouquets,   each    containing    5 
roses,  can  you  make  with  35  roses  ? 

9.  A  lady  bought  5  cups  for  40  cents:  what  did 
one  cup  cost  ? 

10.  If  5  tables  cost  $45,  what  will  one  table 
cost  ? 

(ii.)         (12.)        (13.)         (14.)         (IS-)         (16.) 

5)15        5)25        5)30        5)35        5)45         5)50 


FIRST  Lxs 

LKSSOX  VI 


6  in    6,   i  time.  6  in  36,  6  times. 

6  "    12,  2  times.  6  "  42,  7       " 

6  <<    18,  3     "'••  6  "  48,  8       - 

6  "    24,  4      "  6  «  54,  9      « 

6  "    30,  5       "  6   "  60,  10      tftf 

1.  How  many  pineapples  at  6  cents  each  can 
be  bonght  for  12  cents  ? 

2.  I  paid  1  8  cents  for  6  kites:  what  was  the 
cost  of  each  ? 

3.  If  6  pounds  of  flour  cost  24  cents,  what  is 
the  cost  of  one.  pound  ? 

4.  How  many  days  will  30  apples  last,  if  you 
eat  6  each  day  ? 

5.  How  many  boards  6  feet  long  will   reach 
across  a  yard  which  is  36  feet  in  length  ? 

6.  If  a  stage  holds  6  persons,  how  many  stages 
will  be  required  to  carry  42  persons  ? 

7.  If  48  trees  are  planted  in  6  equal  rows,  how 
many  trees  will  there  be  in  each  row  ? 

8.  If  James  saves  6  cents  a  week,  how  long  will 
it  take  him  to  save  54  cents  ? 

9.  If   6   trunks   cost   $60,   what  is   the   price 
of  one  ? 

10.  Continue  :  6+6=1.    12+6=2.   18+6=3. 

(11.)         (12.)         (13.)         (14.)        (15.)         (16.) 
6)12         6)24         6)30         6)42         6)54         6)60 


FIRST  LESSONS  ix  NUMBERS. 
LESSON  VII. 


7 

in 

7, 

i 

time. 

7 

in 

42, 

6 

times* 

7 

(( 

H, 

2 

times. 

7 

(C 

49? 

7 

ft 

7 

t( 

2I> 

3 

f< 

7 

(  £ 

56, 

8 

a 

7 

a 

28, 

4 

« 

7 

it 

63, 

9 

<e 

7 

(( 

35. 

5 

tt 

7 

a 

7°, 

io 

" 

1.  If  i  pound  of  sugar  costs  7  cents,  how  many 
pounds  can  be  bought  for  14  cents  ? 

2.  7  days  make  a  week :  how  many  weeks  in 
21  days  ? 

3.  I  tied  28  cherries  in  bunches  of  7  cherries 
each :  how  many  bunches  did  I  make  ? 

4.  How  many  sevens  in  35  ?    How  many  fives 

in  35  ? 

5.  If  7  pencils  cost  42  cents,  what  will  one 

cost  ? 

6.  At  $7  each,  how  many  calves  can  be  bought 
for  49  dollars  ? 

7.  How  many  yards  at  7  cents  a  yard  can  be 
bought  for  56  cents  ? 

8.  63  is  seven  times  what  number  ? 

9.  John  spent  63  cents  in  one  week :  how  much 
did  he  spend  each  day  ? 

10.  How  many  times  $7  is  $49  ? 

11.  Continue:  7—7=1.    14+7=2..  21+7=8. 

(12.)         (13.)         (14.)         (is-)        (16.)        (17.) 
7)U'        7)21         7)28         7)35         7)49         7)70 


74  FIKST  LESSOXS  ix  XU 

LESSOX   VIII. 


8  in    8/1  time.         8  in  48,     6  times. 
8  "    16,  2  times.       8  "   56,     7      " 
8  "    24,  3      "  3  «   64,     8      « 

8  "    32,  4      "  8  "    72,     9      " 

8  "    40,  5      "  8  "   So,   10      " 

1.  At  8  cents  a  quart,  how  many  quarts  of  milk 
can  be  bought  for  16  cents  ? 

2.  If  one  slate  cost  8  cents,  how  many  can  be 
bought  for  24  cents  ? 

3.  8  boys  earned  32  cents :  what  was  each  boy's 
share  ? 

4.  I  paid  40  cents  for  8  bouquets :  what  was 
the  price  of  one  ? 

5.  8  quarts  make  a  peck :  how  many  pecks  in 
48  quarts  of  corn  ? 

6.  8  pounds  of  oatmeal  cost   56  cents :  what 
was  the  price  of  one  pound  ? 

7.  How  many  pews,  each  seating  8  children, 
will  seat  64  boys  ? 

8.  How  many  eights  in  72  ?     In  80  ?      In  88  ? 
In  96  ?     In  800  ?    '• 

9.  How  many  yards  of  velvet  at  88  a  yard  can 
be  bought  for  872  ? 

10.  How  many  times  88  is  840  ? 

11.  Continue:  8+8=1.    16+8=2.   24+8-3. 

(12.)         (13.)         (14.)         (15.)         (16.)        (17.) 


> 


LESSORS  ix  NCMBEHS. 


LESSON  IX. 


9  in 

9, 

I 

time. 

10  ill 

IO, 

i 

time. 

9  " 

18, 

2 

times. 

10  *' 

20, 

2 

times. 

9  " 

27, 

3 

a 

10     '  *' 

30, 

3 

" 

9  " 

36, 

4 

10    " 

40, 

4 

" 

9  " 

45. 

5 

a 

10    4i 

5°, 

5 

a 

9  " 

54, 

6 

a 

10   "• 

60, 

6 

a 

9  " 

63, 

7 

a 

10  " 

70, 

7 

" 

9  " 

72, 

8 

ii 

I  O 

80, 

8 

a 

9  " 

81, 

9 

a 

10     " 

90, 

9 

tt 

9  " 

90, 

10 

ii 

10    " 

100, 

10 

ff 

LESSON    X. 

ii  in 

Ir, 

i 

time.          12  in 

I2> 

i 

time. 

n  " 

22, 

2 

times.        12  " 

24, 

2 

times. 

ii  " 

33, 

3 

12    " 

36, 

3 

a 

ii  " 

44, 

4 

"                    12     '* 

48, 

4 

" 

ii  " 

55, 

5 

a 

12     " 

60, 

5 

« 

ii  " 

66, 

6 

66 

12     " 

72, 

6 

" 

a  " 

77, 

7 

ii 

12     " 

84, 

7 

" 

ii  " 

88, 

8 

it 

12     " 

96, 

8 

a 

n  " 

99. 

9 

ii 

12    " 

1  08, 

9 

a 

ii  " 

IIO, 

10 

ii 

12     " 

120, 

10 

66 

ii  " 

121, 

1  1 

ii                          j  fj      it 

132, 

n 

a 

ii  " 

!32, 

12 

it                          12      « 

T44, 

12 

n 

70  FIRST  LESSORS  IN 

LESSON  XL 


When  the  divisor   consists  of  one  figure. 

How  many  chairs,  at  $2  each,  can  be  bought 
for  §246  ? 

ANALYSIS.  —  i.  Write  the  divisor  to  the        Slate  work. 
left  of  the  dividend,  with  a  curve  line  be-  2)246 

tween  them,   and  begin  at  the  left  to    Chairs  123  Ans. 
divide. 

2.  2  is  contained  in  2  hundreds  i  hundred  times  ;  write 
the  i  under  the  figure  divided,  for  it  is  of  the  same  order. 

3.  2  is  contained  in  4  tens,  2  tens  times  ;  write  the  2 
under  the  figure  divided,  for  it  is  of  the  same  order. 

4.  Continue  thus  until  each  figure  is  divided. 
Hence  the  quotient  is  123. 


To  divide  by  one  figure  when  the  divisor  is 
not  contained  an  even  number  of  times. 

Slate  work. 

ANALYSIS.— i.  Write  the  divisor  to  the  left       4)3369 
of  the  dividend,  with  a  curve  line  between  them.  842^ 

2.  4  is  not  contained  hi  3  thousands  any  thousands  times  ; 
unite  the  3  thousands  and  3  hundreds,  making  33  hun- 
dreds.    4  is  contained  in  33  hundreds,  8  hundred  times, 
and  a  remainder  ;  write  the  8  under  the  figure  divided. 

3.  i  hundred  and  6  tens  make  16  tens.    4  is  contained  in 
1 6  tens,  4  tens  times  ;  write  the  4  under  the  figure  divided. 

4.  4  is  contained  in  9  units,  2  times  ;  write  the  2  under 
the  figure  divided.    9  is  the  last  figure  ;  write  the  last  re- 
mainder over  the  division,  and  annex  it  to  the  quotient. 

Hence  the  quotient  is  8424. 


LESSONS  IN  NUMBERS.  Tl 

LESSON  XII. 

When  the  divisor  exceeds  12. 

Divide  48352  by  32- 

1.  32  is  contained    in    48    thousands,      32)48352(1511 
i  thousand    time.     Write    the    i    thou-          32"  * 
sand    in     the     quotient  ;    multiply    the 

divisor  by  it ;  subtract  the  product  from  163 

the  figures  divided,  and  annex  to  the  re-  160 
mainder  the  next  figure  of  the  dividend 
for  a  partial  dividend.  35 

2.  32  is  contained   in  163  hundreds,  5  32 
hundreds  times.      Write  the  5  hundreds 

in  the  quotient,  and  continue  the  above  32 

process  until  all  the  figures  of  the  dividend  32 

have  been  brought  down. 
Hence  the  quotient  is  1511. 

11ULE   FOR   DIVISION. 

1 .  Write  the  divisor  to  the  left  of  the  dividend,  and 
draw  a  curve  line  for  the  quotient. 

2.  Find  Jww  many  times  the  divisor  is  contained  in, 
the  least  number  of  left-hand  figures  that  will  contain 
it,  and  write  the  result  in  the  quotient. 

3.  Multiply  the  divisor  by  the  quotient  figure  ;  sub- 
tract the  product  from  the  figures  divided,  and  to  the 
remainder  annex  the  next  figure  of  the  dividend  for  a 
partial  dividend. 

4.  Divide  as  before,  until  all  the  figures  of  the  divi- 
dend have  been  brought  down. 

5.  If  any  partial  dividend  ivill  not  contain   the 
divisor,  tvrite  a  cipher  in  the  quotient,  annex  the  next 
figure  of  the  dividend  to  the  partial  divisor,  and  divide 
as  before. 

6.  If  tJiere  be  a  final  remainder,  ivrite  it  over  the 
divisor,  and  annex  it  to  the  quotient. 

Proof, — Multiply  the  quotient  by  the  divisor. 


78  FIRST  LESSORS  iy  ^' 

STATES   MONEY. 


A  coin  is  a  piece  of  metal  bearing  n  legal 
stamp.  Each  coin  lias  a  lixed  value. 

Paper  money  consists  of  notes  and  bills  issued 
by  a  government  or  a  bank,  as  substitutes  for 
coin.  Notes  and  bills  are  promises  to  pay  stated 
sums  of  money. 

United  States  Money  is  the  legal  currency  of 
the  United  States. 

The  denominations  are  eagles,  dollars,  dimes, 
cents,  and  mills. 


The  Unit  of  United 
States  money  is  the 
Dollar. 


TABLE. 

10  mills  (m.)  make  i  cent,  ct. 

10  cents  "      i  dime,  d. 

10  dimes  "      i  dollar,  8. 

10  dollars  "      i  eagle,  E. 

The  coin  of  the  United  States  consists  of  gold, 
silver,  nickel,  and  bronze. 

The  gold  coins  are  the  double-eagle,  eagle,  half- 
eagle,  quarter-eagle,  three  dollars,  and  one-dollar 
pieces. 

The  silver  coins  are  the  trade  dollar,  half-dollar, 
quarter -dollar,  and  dime. 

The  nickel  coins  are  the  live-cent  and  three- 
cent  pieces. 

The  bronze  coins  are  the  two-cent  and  one- 
cent  pieces. 


FIRST  LESSORS  IN 


ENGLISH    MONEY. 

English  Sterling  Money  is  the  legal  currency  of 
Great  Britain. 

The  denominations  are  pounds,  shillings,  pence, 
and  farthings. 


The    Unit     of 
["English  money  is 
the    pound   ster- 
ling or  Sovereign. 


TABLE. 


4  farthings  (far.)  make  i  penny,      cl. 


12  pence 
20  shillings 

2  shillings— i  florin. 
5        " 


i  crown, 
i  guinea. 


i  shilling, 
\  i  pound,      £, 
/  i  sovereign,  sov. 

i  pound  —  $4.866^. 

i  shilling  =2 4  cents 

i  penny  =  2  cents. 


FBENCH  MONEY. 

French  Money  is  the  legal  currency  of  France. 

The  denomi- 
nations used  in 
business  are  na- 
poleons, francs, 
and  centimes. 

The  Unit  of 
French  money 
is  the  Franc. 

The  value  of  the  franc  is  18  cents  and  6  mills. 


80  FIHST  LESSORS  AY  LU 


TEOY    WEIGHT. 

The  Standard  Unit  of  weight  in  the  United 
States  is  the  Troy  pound. 

Troy  Weight  is  used  in  weighing  gold,  silver, 
coin,  jewels,  etc. 

The  denominations  are  pounds,  ounce*?,  penny- 
weights, and  grains. 

TABLE, 

24  grains  (gr.)    make  i  pennyweight,  pwt. 
20  pennyweights     ••    i  ounce,  oz. 

12  ounces  '  "     i  pound,  Ib. 

3-J-  grains  "     i  carat. 

5760  grains  *'•'     i  pound. 


|L 
i  grain.     24  grains.     480  grains.     5760  grains. 

APOTHECARY    WEIGHT. 

Apothecary  Weight  is  used  in  preparing 
medicine,  but  all  drugs  are  bought  and  sold 
in  large  quantities  by  Avoirdupois  Weight, 

The  denominations  are  pounds,  ounces,  drams, 
scruples,  and  grains. 

TABLE. 
20  grains  (gr.)  make  i  scruple.       $. 

3  scruple?  "  i  dram.  3. 

^  drams  >;  i  ounce.  § . 

12  ounces  "  T  ])oiuid.  Ib. 

5760  grains  *'*  i  pound. 


FIRST  LESSORS  IN  LU 


81 


The  pound,  ounce,  and  grain  of  this  weight 
ure  the  same  as  those  of  Troy  weight,  the  differ- 
ence being  in  the  subdivision  of  the  ounce. 


60  gr. 


480  gr.  5760  gr. 

AVOIRDUPOIS   WEIGHT. 


Avoirdupois  Weight 

is  used  to  weigh  all 
coarse  and  heavy  ar- 
ticles. 

The  denominations 
are  tons,  hundred- 
weights, quarters, 
pounds,  and  ounces. 

The  Long  ton  is  used 
in  the  United  States 
Custom-houses  and  in 
selling  coal  at  the 
mines. 


1 6  ounces  (oz.)      make 
25  pounds  " 

4  quarters  *' 

20  hundredweight    " 

2240  pounds 

7000  Troy  grains          " 


Not  used. 


pound,  Ib. 

quarter,  qr. 

hundred  weight,  cwt. 
ton,  T. 

Long  ton,          L.  T. 
avoirdupois  pound. 


437  Jgr- 


7000  gr. 


FIRST  LESSOXS  IN 


LIQUID   OK   WINE   MEASURE. 

Liquid  Measure  is  used  in  measuring  wine, 
liquor,  milk,  water,  etc. 

The  denominations  are  hogsheads,  barrels, 
gallons,  quarts,  pints,  and  gills. 

TABLE. 


4  gills  (gi.)       n 
2  pints 
4  quarts 
231  cubic  inches 
31  1  gallons 
2  barrels 

lake  i  pint, 
i  quart, 
i  gallon, 
i  gallon. 
4       i  barrel, 
i  hogshead, 

pt. 
qt. 
gal. 

bbl. 
hhd. 

Barrels  and  hogsheads  are  not  fixed  measures. 


DRY   MEASURE. 

Dry  Measure  is  used  in  measuring  grain,  fruit, 
salt,  etc. 

The  denominations  are  bushels,  pecks,  quarts, 
and  pints. 

TABLE. 


2  pints  (pt.)  make 

quart, 

qt. 

8  quarts            *•' 

peck, 

nk. 

4  pecks 

bushel, 

1m. 

36  bushels 

chaldron, 

d. 

2  quarts             " 

small  measure. 

LESSORS  rx 


The  standard  bushel  contains  2150.42  cubic 
inches.  It  is  a  cylindrical  measure,  i8|  inches 
in  diameter  and  8  inches  deep. 


LOKG   MEASUKE. 

Long  Measure  is  used  in  measuring  lines  and 
distances. 

The  denominations  are  leagues,  miles,  furlongs, 
rods,  yards,  feet,  and  inches. 


TABLE. 

12    inches  (in.)  make  i  foot, 
3 


feet 
„•  feet 

5i  yards 
40    rods 

8    furlongs 
5280    feet 
3    miles 


ft. 

yd. 

rd. 


i  yard, 

i  rod, 

i  rod. 

i  furlong,     fur. 

i  mile,  "       mi. 

i  mile. 

i  league. 

OTHEK   DENOMINATIONS. 

4    inches  make  i  hand,         h. 
6    feet          "      i  fathom,     fath. 
i-t  miles       "      i  knot,         k. 


1 1 1 1 1 1 1 1 1 1 1 1  1 1 1 


Cloth  Measure  is  no  longer  used.  In  measur- 
ing dry-goods,  etc.,  the  yard  is  divided  into 
halves,'  quarters,  eighth?,  etc. 


84  FIRST  LESSONS  /.v  Jfni 

SURVEYORS'  LONG  MEASURE. 

Surveyors'  Long  Measure  is  used  in  laying  out 
roads  and  measuring  land. 

The  unit  of  measure  is  Gunter's  Chain.  It  is 
66  feet  long,  and  consistsof  100  links.  80  chains 
make  one  mile. 

SURFACE,  OR  SQUARE  MEASURE. 

A  surface  has  two  dimensions 
— length  and  breadth. 


A  square  is  a  plane  figure 
having  four  equal  sides  and  four 
right  angles. 

Surface,  or  Square  Measure  is 
used  in  measuring  the  surface 
of  land,  boards,  plastering,  etc. 

The  denominations  are  square  miles,  acres, 
square  rods,  square  yards,  square  feet,  and  square 
inches. 

TABLE. 

144  square  inches  (sq.in.)  make  i  square  foot,sq.ft. 
9    square  feet  make  i  square  yard,    sq.  yd. 
30^  square  yards    "     i  square  rod,      sq.  rd. 
272!  square  feet      "     i  square  rod. 
1 60    square  rods      "     i  square  acre,    A. 
640    acres  ''     i  square  mile,    sq. 


mi. 


SURVEYORS'  SQUARE   MEASURE. 

Surveyors'  Square  Measure  is  used  by  surveyors 
in  computing  the  area  or  surface  of  lands. 


FIRST  LKSSOXS  ix 


TABU-:. 

1 6  square  rods  make  i  square  chain,  sq.  eh. 
10  square  chains  "    i  acre,  A. 

640  acres  make  i  square  mile  or  section. 
36  square  miles  make  i  township. 

Government  lands  are  divided  into  townships 
by  parallels  and  meridians. 

CUBIC,  OR  SOLID  MEASURE. 

A  Solid  has  three  dimensions — length,  breadth, 
and  thickness. 

A  Cube  is  a  body  bounded  by  six  equal  squares, 
called  faces. 

The  Volume,  or  contents  of  a  solid  is  the  space 
included  within  the  surfaces  which  bound  it. 

Cubic  or  Solid  Measure  is  used  in  computing 
the  volume  of  solids,  and  the  capacity  of  rooms, 
cisterns,  ships,  etc. 

The  denominations  are  cubic  yards,  cubic  feet, 
and  cubic  inches. 

TABLE. 

1 728  cubic  inches  (en.  in.)  make  i  cubic  foot,  cu.fr. 
27  cubic  feet  "     i  cubic  yard,cu.yd. 

1 28  cubic  feet  "     i  cord  of  wood. 


A  Cord 
of  Wood 

i.s  a  pile 
8  feet 
long-,  4 
fr.  wide, 
and  4 
ft.  hio-h. 


FIRST  LFXSOXS  i.\  A'r.w;/ 


TIME    MEASURE. 

The  denominations  of  Time  Measure  are  years. 
months,  days,  hours,  minutes,  and  seconds. 


TABLE. 

60  seconds  (sec.)  make  i  minute,  min. 

60  minutes  "  i  hour,  hr. 

24  hours  "  i  day.  d. 

7  days  "  i  week,  w. 

30  or  31  days  "         month.  mo. 

12  months 


52  weeks 

365  days 

366  days 
100  years 


year,          y. 
year. 

common  year, 
leap  year, 
centurv. 


The  exact  length  of  a  solar  year  is  365  days, 
5  hrs..  48  min.,  46  sec.,  or  nearly  365!  days. 


NAMES     OF    THE    MONTHS. 

1.  January  (Jan.)  has  31  days. 

2.  February  (Feb.)  "  28  days. 

3.  March    '  (Mar.)  "  31  days. 

4.  April  (Apr.)  "  30  days. 

5.  May  (May)  "  31  days. 

6.  June  (June)  "  30  days. 

7.  July  (July)  "  31  days. 

8.  August  (Aug.)  "  31  days. 

9.  September  (Sept.)  "  30  days. 

10.  October  (Oct.)  "  31  days. 

11.  Xovember  (Xoy.)  '*  30  days. 

12.  December  (Dec.)  "  31  days. 


FIRST  LESSONS  IN  NUMBERS.          87 

Thirty  days  hath  September, 
April,  June,  and  November ; 
All  the  rest  have  thirty-one,  except  February. 

CIRCULAR,  OR  ANGULAR  MEASURE. 

A  Circle  is  a  plane  figure  bounded  by  a  curve 
line,  every  point  of  which  is  equally  distant  from 
a  point  within,  called  the  centre. 

A  Circumference  is  the  curve  line  which  bounds 
the  circle. 

The  circumference  is  3j-  times  the  diameter. 

An  Arc  is  any  part  of  the  circumference. 

A  Radius  is  any  straight  line  drawn  from  the 
centre  to  the  circumference. 

A  Diameter  is  a  straight  line  drawn  through  the 
centre,  and  terminated  both  ways  by  the  circum- 
ference. 

An  Angle  is  the  difference  in  the  direction  of 
two  lines  drawn  f  1:0111  the  same  point,  called  the 
Vortex. 

Circular,  or  Angular  Measure  is  used  in  measur- 
ing angles  and  arcs  of  circles.  It  is  used  in 
astronomy,  geography,  navigation,  surveying, 
and  for  calculating  difference  of  time. 

TABLE. 

60  seconds  (")  make  i  minute,       ' 

60  minutes  "      i  degree, 

90  degrees  "      i  quadrant,    quad. 

360  degrees  "      i  circle. 

69!  miles  •'*      i  degree  of  latitude. 


FIRST  LKSSOXS  IN  XT 
MISCELLANEOUS    T A  B  LES. 

POUXTTXO. 


12  units 

make 

i  dozen 

t 

i2  dozen 

u 

i  gross. 

12  gross 

<.- 

i  great 

gross. 

20  units 

£.' 

i  score. 

24  sheets  make  i  quire.     2  reams  make  i  bundle. 
20  quires      "      i  ream.     5  bundles  '*     i  bale. 


YA  02444 


102 


THE  UNIVERSITY  OF  CALIFORNIA  LIBRARY 


VTHOLIG  JcHC 


2O 
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CATHOLIC  PUUII 
1    pared  to  suppiy  Ctuhol.c  Col;  and 

Schools  with  everytlnnp;  required  for  use  in  the 
room,  ;  eg. 

;  on  hand  of  flio  following*  !>o< 
Young  Catholic's  Ulv  ;  mar.  ....  ...... 

"  Speller 

First  Reader.  .  ........ 

'  Second  Reader.  ... 

"  "  Third  Reader.  .  . 

"  "  Fourth  Reader  .  .  ^75 

"  Fifth  Reader.  ...  .....  "   1  25 

<s  Sixth  Reader  ..........     1  5O 

Catholic  Young  Ladies'  Reader  ......  ..............      1  25 

Fleury's  Historical  Catechisrir.^.  Abridged  by  Forn 
Formby's    Ilhistralsri    Bible  an  I  Olrarch    History. 

cdiiiou.     With  Questions. 
Mylius's  History  of  Ea^laid.     Continued  down  - 

sent  Time  by  .  .  LL.D:% 

Q-ahan's  Chu  .1  iau-%1  u 

Time  by  J.  G.  Shea,  LL.D. 
Fredet's  Ancient  History. 
ct        Modera  History. 
Catechism  rf  Perseverance. 
Reeve's  Bible  History. 
Kerney'3  First  Class  Book  of  History. 
Kerney's  Compendium  of-  Ancient  and  Modem  History. 
Iiingard's  England    abridged. 

of  Philosophy,  by  Hill. 


Pens,  Ink,  Paper,  Slab, 


sis, 


Anything  orderedvrand  not  in  sto6k  will  bs  pro^ 
lowest  \ 


Tlic  Cafliolip  PuI>Hcatioii  Sod<- 

LAWRBNOE  KEHOS, 

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